A256649 29-gonal pyramidal numbers: a(n) = n*(n+1)*(9*n-8)/2.

0, 1, 30, 114, 280, 555, 966, 1540, 2304, 3285, 4510, 6006, 7800, 9919, 12390, 15240, 18496, 22185, 26334, 30970, 36120, 41811, 48070, 54924, 62400, 70525, 79326, 88830, 99064, 110055, 121830, 134416, 147840, 162129, 177310, 193410, 210456, 228475, 247494

Offset: 0

Author

Luciano Ancora, Apr 07 2015

Keywords

• nonn
• easy

Comments

See comments in A256645.

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (27th 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 A255187.

Cf. similar sequences listed in A237616.

Cf. A000292, A256645.

Programs

Magma

[n*(n+1)*(9*n-8)/2: n in [0..50]]; // Vincenzo Librandi, Apr 08 2015

Mathematica

Table[n (n + 1)(9 n - 8)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 30, 114}, 40] (* Vincenzo Librandi, Apr 08 2015 *)

Formula

G.f.: x*(1 + 26*x)/(1 - x)^4.

a(n) = A000292(n) + 26*A000292(n-1).

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

E.g.f.: exp(x)*x*(2 + 28*x + 9*x^2)/2.

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