A253459 Indices of centered square numbers (A001844) which are also centered heptagonal numbers (A069099).

1, 21, 148, 5208, 37465, 1322685, 9515836, 335956656, 2416984753, 85331667813, 613904611300, 21673907667720, 155929354285321, 5505087215932941, 39605442083860108, 1398270478939299168, 10059626359946181985, 355155196563366055605, 2555105489984246363956

Offset: 1

Author

Colin Barker, Jan 01 2015

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 4*x^2 - 7*y^2 - 4*x + 7*y = 0, the corresponding values of y being A253460.

Examples

			21 is in the sequence because the 21st centered square number is 841, which is also the 16th centered heptagonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..832
• Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

Crossrefs

Cf. A001844, A069099, A253460, A253599.

Programs

PARI

Vec(x*(20*x^3+127*x^2-20*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(20*x^3+127*x^2-20*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).