A256716 a(n) = n*(n+1)*(22*n-19)/6.

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

Offset

0,3

Comments

This sequence is related to the tridecagonal numbers (A051865) by a(n) = n*A051865(n) - Sum_{i=0..n-1} A051865(i).

References

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (22nd row of the table).

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

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.

Mathematica

Table[n (n + 1) (22 n - 19)/6, {n, 0, 40}]

Prog

(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]];

Crossrefs

Partial sums of A051876.

Cf. similar sequences listed in A237616.

Cf. A051865.

Sequence in context: A280297 A090659 A010013 * A063769 A099771 A266818

Adjacent sequences: A256713 A256714 A256715 * A256717 A256718 A256719

Keyword

nonn,easy

Author

Bruno Berselli, Apr 09 2015

Status

approved