A213846 Antidiagonal sums of the convolution array A213844.

3, 23, 90, 250, 565, 1113, 1988, 3300, 5175, 7755, 11198, 15678, 21385, 28525, 37320, 48008, 60843, 76095, 94050, 115010, 139293, 167233, 199180, 235500, 276575, 322803, 374598, 432390, 496625, 567765, 646288, 732688, 827475, 931175, 1044330, 1167498, 1301253, 1446185, 1602900, 1772020

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (2/3)*n^4 + n^3 + (5/6)*n^2 + (1/2)*n. - Corrected by Christian Krause, Jan 25 2026

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

G.f.: f(x)/g(x), where f(x) = x*(3 + 8*x + 5*x^2) and g(x) = (1-x)^5.

Mathematica

(* See A213844. *)
A213846[n_] := n*(n + 1)*(4*n^2 + 2*n + 3)/6; Array[A213846, 50] (* or *)
LinearRecurrence[{5, -10, 10, -5, 1}, {3, 23, 90, 250, 565}, 50] (* Paolo Xausa, Apr 05 2026 *)

Crossrefs

Cf. A213844.

Sequence in context: A024196 A196339 A196318 * A376963 A301580 A112459

Adjacent sequences: A213843 A213844 A213845 * A213847 A213848 A213849

Keyword

nonn,easy

Author

Clark Kimberling, Jul 05 2012

Status

approved