A253821 Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448).

1, 181, 589, 208489, 679321, 240595741, 783935461, 277647276241, 904660842289, 320404716185989, 1043977828065661, 369746764831354681, 1204749508926930121, 426687446210667115501, 1390279889323849293589, 492396943180345019933089, 1604381787530213157871201

Offset: 1

Author

Colin Barker, Jan 14 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of y being A253822.

Examples

			181 is in the sequence because the 181st octagonal number is 97921, which is also the 256th centered triangular 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, A253822, A253823.

Programs

PARI

Vec(-x*(x^4+180*x^3-746*x^2+180*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*(x^4+180*x^3-746*x^2+180*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).