A251863 Numbers n such that the sum of the octagonal numbers N(n), N(n+1) and N(n+2) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) for some m.

2, 147, 3102, 170407, 3580474, 196650299, 4131864662, 226934275407, 4768168240242, 261881957170147, 5502462017375374, 302211551640074999, 6349836399882942122, 348751868710689379467, 7327705703002897834182, 402459354280583903830687

Offset

1,1

Comments

Also nonnegative integers x in the solutions to 18*x^2-9*y^2+24*x-15*y+6 = 0, the corresponding values of y being A251864.

Links

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f: x*(x^4+25*x^3-647*x^2-145*x-2) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

2 is in the sequence because N(2)+N(3)+N(4) = 8+21+40 = 69 = 12+22+35 = P(3)+P(4)+P(5).

Prog

(PARI) Vec(x*(x^4+25*x^3-647*x^2-145*x-2)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000567, A251864.

Sequence in context: A214910 A328228 A316889 * A110624 A177319 A333495

Adjacent sequences: A251860 A251861 A251862 * A251864 A251865 A251866

Keyword

nonn,easy

Author

Colin Barker, Dec 10 2014

Status

approved