A253447 Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099).

1, 15, 435, 13021, 390181, 11692395, 350381655, 10499757241, 314642335561, 9428770309575, 282548466951675, 8467025238240661, 253728208680268141, 7603379235169803555, 227847648846413838495, 6827826086157245351281, 204606934935870946699921

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to 7*x^2 - 8*y^2 - 7*x + 8*y = 0, the corresponding values of x being A253446.

Examples

			15 is in the sequence because the 15th centered octagonal number is 841, which is also the 16th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..678
• Giovanni Lucca, Circle Chains Inscribed in Symmetrical Lenses and Integer Sequences, Forum Geometricorum, Volume 16 (2016) 419-427.
• Index entries for linear recurrences with constant coefficients, signature (31,-31,1).

Crossrefs

Cf. A016754, A069099, A253446, A253514.

Programs

PARI

Vec(-x*(x^2-16*x+1)/((x-1)*(x^2-30*x+1)) + O(x^100))

Formula

a(n) = 31*a(n-1)-31*a(n-2)+a(n-3).

G.f.: -x*(x^2-16*x+1) / ((x-1)*(x^2-30*x+1)).

a(n) = (8+(4+sqrt(14))*(15+4*sqrt(14))^(-n)-(-4+sqrt(14))*(15+4*sqrt(14))^n)/16. - Colin Barker, Mar 03 2016