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A254229
Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566).
3
1, 46, 207, 14652, 66493, 4717738, 21410379, 1519096824, 6894075385, 489144459430, 2219870863431, 157502996839476, 714791523949237, 50715475837851682, 230160650840790723, 16330225716791401968, 74111014779210663409, 5258281965330993581854
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 5*x^2 - 4*y^2 - 3*x + 4*y - 2 = 0, the corresponding values of x being A254228.
FORMULA
a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(45*x^3+161*x^2-45*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).
EXAMPLE
46 is in the sequence because the 46th centered square number is 4141, which is also the 41st heptagonal number.
MATHEMATICA
LinearRecurrence[{1, 322, -322, -1, 1}, {1, 46, 207, 14652, 66493}, 20] (* Harvey P. Dale, Sep 19 2022 *)
PROG
(PARI) Vec(x*(45*x^3+161*x^2-45*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 27 2015
STATUS
approved