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

1,2

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.

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).

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

Example

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

Prog

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

Crossrefs

Cf. A016754, A069099, A253446, A253514.

Sequence in context: A133791 A361284 A323781 * A302112 A262077 A225492

Adjacent sequences: A253444 A253445 A253446 * A253448 A253449 A253450

Keyword

nonn,easy

Author

Colin Barker, Jan 01 2015

Status

approved