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

%I #20 Aug 08 2021 01:53:38

%S 0,0,0,1,6,12,32,57,73,144,210,255,394,516,520,833,1032,1182,1518,

%T 1809,1927,2500,2904,3205,3836,4368,4768,5577,6258,6550,7780,8625,

%U 9265,10496,11526,12403,13782,15012,15996,17689,19140,20218,22274,23961,25309,27588,29532,31209,33688

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

%C 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).

%C 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

%F a(n) = A007678(2*n)/(2*n) - (n-1)^2. - _M. F. Hasler_, Aug 06 2021

%o (PARI) apply( {A085611(n)=A007678(2*n)/(2*n)-(n-1)^2}, [1..40]) \\ _M. F. Hasler_, Aug 05 2021

%Y Cf. A007678, A006533, A000290.

%K nonn

%O 1,5

%A _Jon Perry_, Jul 08 2003

%E The last term seemed to be corrupted and has now been deleted. - _N. J. A. Sloane_, Oct 29 2006

%E Edited and more terms from _M. F. Hasler_, Aug 06 2021

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Last modified April 25 01:06 EDT 2024. Contains 371964 sequences. (Running on oeis4.)