A256648 28-gonal pyramidal numbers: a(n) = n*(n+1)*(26*n-23)/6.

0, 1, 29, 110, 270, 535, 931, 1484, 2220, 3165, 4345, 5786, 7514, 9555, 11935, 14680, 17816, 21369, 25365, 29830, 34790, 40271, 46299, 52900, 60100, 67925, 76401, 85554, 95410, 105995, 117335, 129456, 142384, 156145, 170765, 186270, 202686, 220039, 238355

Offset: 0

Author

Luciano Ancora, Apr 07 2015

Keywords

• nonn
• easy

Comments

See comments in A256645.

This sequence is related to A051867 by a(n) = n*A051867(n) - Sum_{i=0..n-1} A051867(i). - Bruno Berselli, Apr 09 2015

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (26th row of the table).

Links

• Luciano Ancora, Table of n, a(n) for n = 0..1000
• Luciano Ancora, Polygonal and Pyramidal numbers, Section 3.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Partial sums of A161935.

Cf. similar sequences listed in A237616.

Cf. A000292, A051867, A256645.

Programs

Magma

[n*(n+1)*(26*n-23)/6: n in [0..50]]; // Vincenzo Librandi, Apr 08 2015

Mathematica

Table[n (n + 1)(26 n - 23)/6, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 29, 110}, 40] (* Vincenzo Librandi, Apr 08 2015 *)

Formula

G.f.: x*(1 + 25*x)/(1 - x)^4.

a(n) = A000292(n) + 25*A000292(n-1).

From Elmo R. Oliveira, Aug 04 2025: (Start)

E.g.f.: exp(x)*x*(6 + 81*x + 26*x^2)/6.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)