A253879 Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217).

1, 9, 136, 2160, 34417, 548505, 8741656, 139317984, 2220346081, 35386219305, 563959162792, 8987960385360, 143243407002961, 2282906551662009, 36383261419589176, 579849276161764800, 9241205157168647617, 147279433238536597065, 2347229726659416905416

Offset: 1

Author

Colin Barker, Jan 17 2015

Keywords

• nonn
• easy

Comments

Also positive integers y in the solutions to x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of x being A253878.

Examples

			9 is in the sequence because the 9th centered heptagonal number is 253, which is also the 22nd triangular number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..832
• Index entries for linear recurrences with constant coefficients, signature (17,-17,1).

Crossrefs

Cf. A000217, A069099, A253878, A253880.

Programs

PARI

Vec(x*(8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^100))

Formula

a(n) = 17*a(n-1)-17*a(n-2)+a(n-3).

G.f.: x*(8*x-1) / ((x-1)*(x^2-16*x+1)).

a(n) = (14-(8-3*sqrt(7))^n*(7+3*sqrt(7))+(-7+3*sqrt(7))*(8+3*sqrt(7))^n)/28. - Colin Barker, Mar 04 2016