Search: id:A022560
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%I A022560
%S A022560 0,1,4,8,16,25,36,48,68,89,112,136,164,193,224,256,304,353,404,456,512,
%T A022560 569,628,688,756,825,896,968,1044,1121,1200,1280,1392,1505,1620,1736,
%U A022560 1856,1977,2100,2224,2356,2489,2624,2760,2900,3041
%N A022560 a(0)=0, a(2n) = 2a(n)+2a(n-1)+n^2+n, a(2n+1) = 4a(n)+(n+1)^2.
%H A022560 R. Stephan, <a href="somedcgf.html">Some divide-and-conquer sequences 
               ...</a>
%H A022560 R. Stephan, <a href="a079944.ps">Table of generating functions</a>
%F A022560 Let a(i, n)=2^{i-1}\lfloor {1\over2}+{n\over 2^i}\rfloor; sequence is 
               a_n=sum_{i=1}a(i, n)(n-a(i, n)).
%F A022560 Second differences give A006519. Also a_1=0 and a_n=\lfloor n^2/4\rfloor 
               + a_{\lfloor n/2\rfloor}+a_{\lceil n/2\rceil}.
%F A022560 G.f.: 1/(1-x)^2 * (x/(1-x) + Sum(k>=1, 2^(k-1)*x^2^k/(1-x^2^k))). - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Apr 17 2003
%F A022560 a(0)=0, a(2n) = 2a(n)+2a(n-1)+n^2+n, a(2n+1) = 4a(n)+(n+1)^2. - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Sep 13 2003
%Y A022560 First differences are in A006520.
%Y A022560 Cf. A070263.
%Y A022560 Sequence in context: A137932 A140466 A161226 this_sequence A003451 A013934 
               A167189
%Y A022560 Adjacent sequences: A022557 A022558 A022559 this_sequence A022561 A022562 
               A022563
%K A022560 nonn
%O A022560 0,3
%A A022560 Andre Kundgen (kundgen(AT)math.uiuc.edu)
%E A022560 More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 13 2003

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