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A257939
x-values in the solutions to x^2 + x = 5*y^2 + y.
2
0, 2, 116, 798, 37512, 257114, 12078908, 82790070, 3889371024, 26658145586, 1252365390980, 8583840088782, 403257766524696, 2763969850442378, 129847748455561292, 889989708002357094, 41810571744924211488, 286573922006908542050, 13462874254117140538004
OFFSET
1,2
FORMULA
a(1) = 0, a(2) = 2, a(3) = 116, a(4) = 798, a(5) = 37512; for n > 5, a(n) = a(n-1) + 322*a(n-2) - 322*a(n-3) - a(n-4) + a(n-5).
a(n) = 322*a(n-2) - a(n-4) + 160.
a(n) = 161*a(n-2) + 360*A257940(n-2) + 116.
G.f.: -2*x^2*(3*x^3+19*x^2+57*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Colin Barker, May 14 2015
MATHEMATICA
LinearRecurrence[{1, 322, -322, -1, 1}, {0, 2, 116, 798, 37512}, 30] (* Vincenzo Librandi, May 15 2015 *)
PROG
(Magma) I:=[0, 2, 116, 798, 37512]; [n le 5 select I[n] else Self(n-1)+322*Self(n-2)-322*Self(n-3)-Self(n-4)+Self(n-5): n in [1..19]];
(PARI) concat(0, Vec(-2*(3*x^3+19*x^2+57*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ Colin Barker, May 14 2015
CROSSREFS
Subsequence of A077259.
Cf. A257940.
Sequence in context: A105327 A260334 A357386 * A203607 A188977 A042681
KEYWORD
nonn,easy
AUTHOR
STATUS
approved