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A256716
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a(n) = n*(n+1)*(22*n-19)/6.
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3
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0, 1, 25, 94, 230, 455, 791, 1260, 1884, 2685, 3685, 4906, 6370, 8099, 10115, 12440, 15096, 18105, 21489, 25270, 29470, 34111, 39215, 44804, 50900, 57525, 64701, 72450, 80794, 89755, 99355, 109616, 120560, 132209, 144585, 157710, 171606, 186295, 201799
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OFFSET
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0,3
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COMMENTS
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This sequence is related to the tridecagonal numbers (A051865) by a(n) = n*A051865(n) - Sum_{i=0..n-1} A051865(i).
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (22nd row of the table).
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LINKS
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FORMULA
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G.f.: x*(1 + 21*x)/(1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=25, a(3)=94.
a(n) = Sum_{i=0..n-1} (n-i)*(22*i+1) for n>0.
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MATHEMATICA
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Table[n (n + 1) (22 n - 19)/6, {n, 0, 40}]
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PROG
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(PARI) vector(40, n, n--; n*(n+1)*(22*n-19)/6)
(Sage) [n*(n+1)*(22*n-19)/6 for n in (0..40)]
(Magma) [n*(n+1)*(22*n-19)/6: n in [0..40]];
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CROSSREFS
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Cf. similar sequences listed in A237616.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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