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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
OFFSET
1,2
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 *)
CROSSREFS
Sequence in context: A266065 A156634 A128788 * A211087 A211091 A124070
KEYWORD
nonn
AUTHOR
Tanya Khovanova & Alexey Radul, Aug 09 2009
EXTENSIONS
Comments turned into formulas. - R. J. Mathar, Oct 21 2009
STATUS
approved