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%I
%S 1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,0,10,0,11,0,12,0,13,0,14,0,15,0,16,
%T 0,17,0,18,0,19,0,20,0,21,0,22,0,23,0,24,0,25,0,26,0,27,0,28,0,29,0,
%U 30,0,31,0,32,0,33,0,34,0,35,0,36,0,37,0,38,0,39,0,40,0,41,0,42,0,43,0
%N Expansion of 1/(1-x^2)^2 (included only for completeness - the policy is always to omit the zeros from such sequences).
%C a(n) = (n+2)(n+3)/2 mod n+2. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 17 2004
%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (0,2,0,-1)
%F Contribution from _Paul Barry_, May 27 2003: (Start)
%F Binomial transform is A045891. Partial sums are A008805. The sequence 0, 1, 0, 2, ... has a(n)=floor((n+2)/2)(1-(-1)^n)/2.
%F a(n)=floor((n+3)/2)(1+(-1)^n)/2. (End)
%F a(n)={[1+(-1)^n]/4}*Sum_{k=0..n}{1+(-1)^k} - _Paolo P. Lava_, Nov 30 2007
%F a(n) = (n+2)*(1+(-1)^n))/4 - Bruno Berselli, Apr 01 2011
%o (MAGMA) [(n+2)*(1+(-1)^n)/4: n in [0..75]]; // Vincenzo Librandi, Apr 02 2011
%o (PARI) a(n)=if(n%2,0,n/2+1) \\ _Charles R Greathouse IV_, Jan 18 2012
%Y Cf. A142150.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_.
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