A256650 30-gonal pyramidal numbers: a(n) = n*(n+1)*(28*n-25)/6.

0, 1, 31, 118, 290, 575, 1001, 1596, 2388, 3405, 4675, 6226, 8086, 10283, 12845, 15800, 19176, 23001, 27303, 32110, 37450, 43351, 49841, 56948, 64700, 73125, 82251, 92106, 102718, 114115, 126325, 139376, 153296, 168113, 183855, 200550, 218226, 236911, 256633

Offset: 0

Author

Luciano Ancora, Apr 07 2015

Keywords

• nonn
• easy

Comments

See comments in A256645.

This sequence is related to A051868 by a(n) = n*A051868(n) - Sum_{i=0..n-1} A051868(i). [Bruno Berselli, Apr 09 2015]

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (28th 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 A254474.

Cf. similar sequences listed in A237616.

Cf. A000292, A051868, A256645.

Programs

Magma

[n*(n+1)*(28*n-25)/6: n in [0..50]]; // Vincenzo Librandi, Apr 08 2015

Mathematica

Table[n (n + 1) (28 n - 25)/6, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 31, 118}, 40] (* Vincenzo Librandi, Apr 08 2015 *)

Formula

G.f.: x*(1 + 27*x)/(1 - x)^4.

a(n) = A000292(n) + 27*A000292(n-1).

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

E.g.f.: exp(x)*x*(6 + 87*x + 28*x^2)/6.

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