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, 218140

Offset: 0

Author

Bruno Berselli, Apr 09 2015

Keywords

• nonn
• easy

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).

Crossrefs

Partial sums of A051876.

Cf. similar sequences listed in A237616.

Cf. A051865.

Programs

Magma

[n*(n+1)*(22*n-19)/6: n in [0..40]];

Mathematica

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

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)]

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.

E.g.f.: exp(x)*x*(6 + 69*x + 22*x^2)/6. - Elmo R. Oliveira, Aug 04 2025