A366478 a(n) = (3*n^4 - 4*n^3 + n^2 + 4*n + 4)/4.

1, 2, 8, 40, 137, 356, 772, 1478, 2585, 4222, 6536, 9692, 13873, 19280, 26132, 34666, 45137, 57818, 73000, 90992, 112121, 136732, 165188, 197870, 235177, 277526, 325352, 379108, 439265, 506312, 580756, 663122, 753953, 853810, 963272, 1082936, 1213417, 1355348, 1509380

Offset

0,2

Comments

This is one-third of the total number of points in the configuration obtained at the n-th stage of A365929.

My derivation of this formula ends by giving a(n) = 1 + n + n^2*(n-1)*(3*n-1)/4, which is a nicer-looking formula than the original definition. - N. J. A. Sloane, Jan 05 2026

Links

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: -(2*x^4+10*x^3+8*x^2-3*x+1)/(x-1)^5. - Alois P. Heinz, Nov 02 2023

From Enrique Navarrete, Jan 04 2026: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

E.g.f.: (1/4)*exp(x)*(3*x^4 + 14*x^3 + 10*x^2 + 4*x + 4). (End)

Mathematica

Table[(3n^4 - 4n^3 + n^2 + 4n + 4) /4, {n, 0, 38}] (* Paul F. Marrero Romero, Nov 02 2023 *)

Crossrefs

Cf. A365929.

Sequence in context: A152458 A087971 A127919 * A074092 A003445 A181326

Adjacent sequences: A366475 A366476 A366477 * A366479 A366480 A366481

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 29 2023

Status

approved