A253304 Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the octagonal number O(m) for some m.

1, 22, 77, 1376, 4785, 85302, 296605, 5287360, 18384737, 327731030, 1139557101, 20314036512, 70634155537, 1259142532726, 4378178086205, 78046522992512, 271376407189185, 4837625283003030, 16820959067643277, 299854721023195360, 1042628085786694001

Offset: 1

Author

Colin Barker, Dec 30 2014

Keywords

• nonn
• easy

Comments

Also positive integers x in the solutions to 5*x^2-3*y^2+2*x+2*y+1 = 0, the corresponding values of y being A253305.

Examples

			1 is in the sequence because H(1)+H(2) = 1+7 = 8 = O(2).
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,62,-62,-1,1).

Crossrefs

Cf. A000566, A000567, A253305.

Programs

Mathematica

LinearRecurrence[{1,62,-62,-1,1},{1,22,77,1376,4785},30] (* Harvey P. Dale, Nov 05 2024 *)

PARI

Vec(x*(3*x^3+7*x^2-21*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))

Formula

a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(3*x^3+7*x^2-21*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).