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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)).
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1
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0, 1, 3, 4, 6, 8, 10, 13, 15, 18, 22, 25, 29, 33, 37, 42, 46, 51, 57, 62, 68, 74, 80, 87, 93, 100, 108, 115, 123, 131, 139, 148, 156, 165, 175, 184, 194, 204, 214, 225, 235, 246
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OFFSET
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1,3
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LINKS
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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
a(n) = floor(1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)(n^2 + 11 n + 32)). - Ivan Neretin, May 20 2018
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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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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MATHEMATICA
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Table[Floor[1/120 n (15 n^4 + 330 n^3 + 2765 n^2 + 10482 n + 15208)/(n + 6)/ (n^2 + 11 n + 32)], {n, 42}] (* Ivan Neretin, May 20 2018 *)
a[ n_] := Quotient[n^2 + 5*n, 8]; (* Michael Somos, Mar 23 2023 *)
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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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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