A372751 a(n) = (3*n^5 + 4*n^3 - n)/6.

1, 21, 139, 554, 1645, 4031, 8631, 16724, 30009, 50665, 81411, 125566, 187109, 270739, 381935, 527016, 713201, 948669, 1242619, 1605330, 2048221, 2583911, 3226279, 3990524, 4893225, 5952401, 7187571, 8619814, 10271829, 12167995, 14334431, 16799056, 19591649

Offset: 1

Author

Kelvin Voskuijl, May 12 2024

Keywords

• nonn
• easy

Comments

Sums of hexagonal numbers (A000384) in successive groups of length 1,2,3,etc, so 1, 6+15, 28+45+66, 91+120+153+190, etc.

Examples

			The hexagonal numbers and their groups summed begin
  1, 6, 15, 28, 45, 66, 91, 120, 153, 190
  \/ \---/  \--------/  \---------------/
  1,   21,     139,            554
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000384 (hexagonal numbers), A002412 (their partial sums).

Cf. A260513 (for triangular numbers), A072474 (for squares), A372583 (for pentagonal numbers), A075664 (cubes).

Programs

Mathematica

A372751[n_] := (3*n^5 + 4*n^3 - n)/6; Array[A372751, 50] (* Paolo Xausa, Jun 19 2024 *)

Formula

From Stefano Spezia, May 12 2024: (Start)

G.f.: x*(1 + 15*x + 28*x^2 + 15*x^3 + x^4)/(1 - x)^6.

E.g.f.: exp(x)*x*(6 + 57*x + 79*x^2 + 30*x^3 + 3*x^4)/6. (End)