A195060 Numbers on the main diagonals and on the axes (x,y) in the square spiral whose vertices are the generalized pentagonal numbers A001318.

0, 1, 2, 3, 5, 6, 7, 9, 12, 13, 15, 18, 22, 24, 26, 30, 35, 37, 40, 45, 51, 54, 57, 63, 70, 73, 77, 84, 92, 96, 100, 108, 117, 121, 126, 135, 145, 150, 155, 165, 176, 181, 187, 198, 210, 216, 222, 234, 247, 253, 260, 273, 287, 294, 301, 315, 330

Offset: 0

Author

Omar E. Pol, Sep 08 2011

Keywords

• nonn

Comments

Union of A001318, A032528 and A045943, without repetitions.

Crossrefs

Cf. A000326, A001318, A005449, A032528, A045943.

Formula

a(2*n) = A001318(n). a(4*n+1) = A032528(n+1). a(4*n+3) = A045943(n+1).

Conjectures: a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) + a(n-8) - 2*a(n-9) + 2*a(n-10) - 2*a(n-11) + a(n-12); g.f.: -x*(1+x^2+x^3-x^4+x^5+x^7-2*x^8+x^11+2*x^9-2*x^10) / ( (1+x)*(x^4+1)*(x^2+1)^2*(x-1)^3 ). - R. J. Mathar, Oct 11 2011