A256647 27-gonal pyramidal numbers: a(n) = n*(n+1)*(25*n-22)/6.

0, 1, 28, 106, 260, 515, 896, 1428, 2136, 3045, 4180, 5566, 7228, 9191, 11480, 14120, 17136, 20553, 24396, 28690, 33460, 38731, 44528, 50876, 57800, 65325, 73476, 82278, 91756, 101935, 112840, 124496, 136928, 150161, 164220, 179130, 194916, 211603, 229216

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 (25th 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 A255186.

Cf. similar sequences listed in A237616.

Cf. A000292, A256645.

Programs

Magma

[n*(n+1)*(25*n-22)/6: n in [0..50]]; // Vincenzo Librandi, Apr 08 2015

Mathematica

Table[n (n + 1) (25 n - 22)/6, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 28, 106}, 40] (* Vincenzo Librandi, Apr 08 2015 *)

Formula

G.f.: x*(1 + 24*x)/(1 - x)^4.

a(n) = A000292(n) + 24*A000292(n-1).

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

E.g.f.: exp(x)*x*(6 + 78*x + 25*x^2)/6.

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