A257940 y-values in the solutions to x^2 + x = 5*y^2 + y.

0, 1, 52, 357, 16776, 114985, 5401852, 37024845, 1739379600, 11921885137, 560074829380, 3838809989301, 180342355680792, 1236084894669817, 58069678454385676, 398015497273691805, 18698256119956506912, 128159754037234091425, 6020780400947540840020

Offset: 1

Author

Arkadiusz Wesolowski, May 13 2015

Keywords

• nonn
• easy

Comments

Also, numbers k such that 2*k^2 + k*(k+1)/2 is a triangular number. Example: 114985 is a term because 2*114985^2 + 114985*114986/2 = 257114*257115/2. - Bruno Berselli, Mar 02 2018

Links

• Colin Barker, Table of n, a(n) for n = 1..798
• Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

Crossrefs

Cf. A257939.

Programs

Magma

I:=[0, 1, 52, 357, 16776]; [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]];

Mathematica

LinearRecurrence[{1, 322, -322, -1, 1}, {0, 1, 52, 357, 16776}, 30] (* Vincenzo Librandi, May 15 2015 *)

PARI

concat(0, Vec((3*x^3+17*x^2-51*x-1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ Colin Barker, May 14 2015

Formula

a(1) = 0, a(2) = 1, a(3) = 52, a(4) = 357, a(5) = 16776; 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) + 32.

a(n) = 72*A257939(n-2) + 161*a(n-2) + 52.

G.f.: x^2*(3*x^3+17*x^2-51*x-1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Colin Barker, May 14 2015