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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

%I

%S 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,

%T 73,77,84,92,96,100,108,117,121,126,135,145,150,155,165,176,181,187,

%U 198,210,216,222,234,247,253,260,273,287,294,301,315,330

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

%C Union of A001318, A032528 and A045943, without repetitions.

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

%F 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

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

%K nonn

%O 0,3

%A _Omar E. Pol_, Sep 08 2011

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Last modified July 29 11:05 EDT 2021. Contains 346344 sequences. (Running on oeis4.)