A085611 Difference between A007678(2n)/(2n) and (n-1)^2.

0, 0, 0, 1, 6, 12, 32, 57, 73, 144, 210, 255, 394, 516, 520, 833, 1032, 1182, 1518, 1809, 1927, 2500, 2904, 3205, 3836, 4368, 4768, 5577, 6258, 6550, 7780, 8625, 9265, 10496, 11526, 12403, 13782, 15012, 15996, 17689, 19140, 20218, 22274, 23961, 25309, 27588, 29532, 31209, 33688

Offset: 1

Author

Jon Perry, Jul 08 2003

Keywords

• nonn

Comments

If we define b(n) by b(n)=local(nr,fn,cn); nr=0; fn=floor(n/2); cn=ceiling(n/2); forstep (i=n,4,-2,nr=nr+(i-2)*fn+(i-4)*cn); nr then a(n) is given by (A007678(2n)-b(2n))/(2n).

This b(n) is given by (n-2)*(2*n^2 - 4*n + 3*(-1)^n - 3)/8 for n > 1. - R. J. Mathar, Oct 18 2013

Crossrefs

Cf. A007678, A006533, A000290.

Programs

PARI

apply( {A085611(n)=A007678(2*n)/(2*n)-(n-1)^2}, [1..40]) \\ M. F. Hasler, Aug 05 2021

Formula

a(n) = A007678(2*n)/(2*n) - (n-1)^2. - M. F. Hasler, Aug 06 2021

Extensions

The last term seemed to be corrupted and has now been deleted. - N. J. A. Sloane, Oct 29 2006

Edited and more terms from M. F. Hasler, Aug 06 2021