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

Author

Colin Barker, Jan 14 2015

Keywords

• nonn
• easy

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.

Examples

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

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).

Crossrefs

Cf. A000567, A005448, A253821, A253823.

Programs

Mathematica

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

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))

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)).