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A164080 Perfect squares one less than a triangular number. 2
0, 9, 324, 11025, 374544, 12723489, 432224100, 14682895929, 498786237504, 16944049179225, 575598885856164, 19553418069930369, 664240615491776400, 22564627508650467249, 766533094678624110084, 26039560591564569275625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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.

CROSSREFS

Sequence in context: A266065 A156634 A128788 * A211087 A211091 A124070

Adjacent sequences: A164077 A164078 A164079 * A164081 A164082 A164083

KEYWORD

nonn

AUTHOR

Tanya Khovanova & Alexey Radul, Aug 09 2009

EXTENSIONS

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

STATUS

approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)