A280070 Indices of 10-gonal numbers (A001107) that are also centered 10-gonal numbers (A062786).

1, 11, 191, 3421, 61381, 1101431, 19764371, 354657241, 6364065961, 114198530051, 2049209474951, 36771572019061, 659839086868141, 11840331991607471, 212466136762066331, 3812550129725586481, 68413436198298490321, 1227629301439647239291, 22028913989715351816911

Offset: 1

Author

Colin Barker, Dec 25 2016

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 4*x^2 - 5*y^2 - 3*x + 5*y - 1 = 0, the corresponding values of y being A133273.

Examples

			11 is in the sequence because the 11th 10-gonal number is 451, which is also the 10th centered 10-gonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..750
• Index entries for linear recurrences with constant coefficients, signature (19,-19,1).

Crossrefs

Cf. A001107, A062786, A128922, A133273.

Programs

PARI

Vec(x*(1 - 8*x + x^2) / ((1 - x)*(1 - 18*x + x^2)) + O(x^30))

Formula

a(n) = (6 + (5+2*sqrt(5))*(9+4*sqrt(5))^(-n) + (5-2*sqrt(5))*(9+4*sqrt(5))^n)/16.

a(n) = 19*a(n-1) - 19*a(n-2) + a(n-3) for n>3.

G.f.: x*(1 - 8*x + x^2) / ((1 - x)*(1 - 18*x + x^2)).