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

0,3

Comments

Union of A001318, A032528 and A045943, without repetitions.

Links

Table of n, a(n) for n=0..56.

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

Crossrefs

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

Sequence in context: A085717 A253083 A108130 * A153763 A345982 A050747

Adjacent sequences: A195057 A195058 A195059 * A195061 A195062 A195063

Keyword

nonn

Author

Omar E. Pol, Sep 08 2011

Status

approved