A164080 Perfect squares one less than a triangular number.

0, 9, 324, 11025, 374544, 12723489, 432224100, 14682895929, 498786237504, 16944049179225, 575598885856164, 19553418069930369, 664240615491776400, 22564627508650467249, 766533094678624110084, 26039560591564569275625

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (35, -35, 1).

Formula

a(n) = A164055(n)-1.

a(n) = A072221(n)*(A072221(n)+1)/2 - 1.

a(n) = 35*a(n-1) -35*a(n-2) +a(n-3) = 9*A001110(n-1). G.f.: 9*x^2*(1+x)/((1-x)*(x^2-34*x+1)). - R. J. Mathar, Oct 21 2009

Example

324=18^2 is a perfect square and 325=A000217(25) is a triangular number. Therefore 324 is in this sequence.

Mathematica

LinearRecurrence[{35, -35, 1}, {0, 9, 324}, 20] (* Harvey P. Dale, Oct 24 2023 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -35, 35]^(n-1)*[0; 9; 324])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A164055, A072221, A001110.

Sequence in context: A266065 A156634 A128788 * A211087 A211091 A124070

Adjacent sequences: A164077 A164078 A164079 * A164081 A164082 A164083

Keyword

nonn,easy

Author

Tanya Khovanova & Alexey Radul, Aug 09 2009

Extensions

Comments turned into formulas. - R. J. Mathar, Oct 21 2009

Status

approved