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| A024182
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Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(3rd elementary symmetric function of 2,3,...,n+4)).
(history;
published version)
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#22 by N. J. A. Sloane at Fri Mar 24 17:42:00 EDT 2023
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#21 by Michael Somos at Thu Mar 23 20:19:27 EDT 2023
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#20 by Michael Somos at Thu Mar 23 20:19:18 EDT 2023
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| FORMULA
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a(n) = floor(n*(n + 5)/8) for all n in Z. - Michael Somos, Mar 23 2023
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| EXAMPLE
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G.f. = x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 10*x^7 + ... - Michael Somos, Mar 23 2023
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| MATHEMATICA
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a[ n_] := Quotient[n^2 + 5*n, 8]; (* Michael Somos, Mar 23 2023 *)
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| PROG
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(PARI) {a(n) = (n^2 + 5*n)\8}; /* Michael Somos, Mar 23 2023 */
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| STATUS
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approved
editing
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Discussion
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| Thu Mar 23
| 20:19
| Michael Somos: Added more info.
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#19 by Bruno Berselli at Mon May 21 06:41:11 EDT 2018
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#18 by Joerg Arndt at Mon May 21 05:24:40 EDT 2018
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#17 by Colin Barker at Mon May 21 04:49:22 EDT 2018
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#16 by Colin Barker at Mon May 21 04:48:07 EDT 2018
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| FORMULA
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Empirical g.f.: x^2*(x^6-2*x^5+2*x^4-2*x^3+x^2-1) / ((x-1)^3*(x^2+1)*(x^4+1)). - Colin Barker, Aug 16 2014
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| STATUS
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proposed
editing
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Discussion
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| Mon May 21
| 04:49
| Colin Barker: I adapted the gf.
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#15 by Muniru A Asiru at Sun May 20 15:17:51 EDT 2018
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#14 by Muniru A Asiru at Sun May 20 15:17:25 EDT 2018
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| MAPLE
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seq(floor((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32))), n=1..50); # Muniru A Asiru, May 20 2018
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| PROG
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(GAP) List([1..50], n->Int((1/120)*n*(15*n^4+330*n^3+2765*n^2+10482*n+15208)/((n+6)*(n^2+11*n+32)))); # Muniru A Asiru, May 20 2018
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| STATUS
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proposed
editing
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#13 by Ivan Neretin at Sun May 20 13:43:56 EDT 2018
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