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

1,2

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.

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

Example

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

Prog

(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))

Crossrefs

Cf. A000567, A005448, A253822, A253823.

Sequence in context: A142391 A142552 A211553 * A154628 A142731 A229877

Adjacent sequences: A253818 A253819 A253820 * A253822 A253823 A253824

Keyword

nonn,easy

Author

Colin Barker, Jan 14 2015

Status

approved