A123198 a(n) = ((n+1)*(2*n-1))^2.

1, 4, 81, 400, 1225, 2916, 5929, 10816, 18225, 28900, 43681, 63504, 89401, 122500, 164025, 215296, 277729, 352836, 442225, 547600, 670761, 813604, 978121, 1166400, 1380625, 1623076, 1896129, 2202256, 2544025, 2924100, 3345241, 3810304, 4322241, 4884100

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = Sum_{k=0..n} (4*k-1)*(4*k^2-2*k-1), n>=0.

G.f.: (1-x+71*x^2+25*x^3)/(1-x)^5. - Colin Barker, Jan 28 2012

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, Feb 21 2026

Maple

a:=n->(n+1)^2*(2*n-1)^2: seq(a(n), n=0..31);

Mathematica

A123198[n_] := ((n+1)*(2*n-1))^2; Array[A123198, 50, 0] (* Paolo Xausa, Aug 21 2025 *)

Crossrefs

Sequence in context: A017006 A394983 A041189 * A202831 A335691 A264197

Adjacent sequences: A123195 A123196 A123197 * A123199 A123200 A123201

Keyword

nonn,easy

Author

Roger L. Bagula, Oct 04 2006

Extensions

Edited by N. J. A. Sloane, Oct 15 2006

Status

approved