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

1,2

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.

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).

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)).

Example

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

Mathematica

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

Prog

(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))

Crossrefs

Cf. A000566, A000567, A253305.

Sequence in context: A282723 A003908 A075252 * A094844 A323251 A010010

Adjacent sequences: A253301 A253302 A253303 * A253305 A253306 A253307

Keyword

nonn,easy

Author

Colin Barker, Dec 30 2014

Status

approved