A253822 Indices of centered triangular numbers (A005448) which are also octagonal numbers (A000567).

1, 256, 833, 294848, 960705, 340253760, 1108652161, 392652543616, 1279383632513, 453120695078528, 1476407603267265, 522900889468077120, 1703773094786790721, 603427173325465917376, 1966152674976353224193, 696354435116698200574208, 2268938483149616833927425

Offset

1,2

Comments

Also positive integers y in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of x being A253821.

Links

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(255*x^3+577*x^2-255*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

256 is in the sequence because the 256th centered triangular number is 97921, which is also the 181st octagonal number.

Mathematica

LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 256, 833, 294848, 960705}, 20] (* Harvey P. Dale, Jul 19 2019 *)

Prog

(PARI) Vec(x*(255*x^3+577*x^2-255*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Crossrefs

Cf. A000567, A005448, A253821, A253823.

Sequence in context: A361176 A203450 A188248 * A258733 A209381 A236987

Adjacent sequences: A253819 A253820 A253821 * A253823 A253824 A253825

Keyword

nonn,easy

Author

Colin Barker, Jan 14 2015

Status

approved