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A022560
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a(0)=0, a(2n) = 2a(n)+2a(n-1)+n^2+n, a(2n+1) = 4a(n)+(n+1)^2.
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2
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0, 1, 4, 8, 16, 25, 36, 48, 68, 89, 112, 136, 164, 193, 224, 256, 304, 353, 404, 456, 512, 569, 628, 688, 756, 825, 896, 968, 1044, 1121, 1200, 1280, 1392, 1505, 1620, 1736, 1856, 1977, 2100, 2224, 2356, 2489, 2624, 2760, 2900, 3041
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| 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)).
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}.
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
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
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CROSSREFS
| First differences are in A006520.
Cf. A070263.
Sequence in context: A137932 A140466 A161226 * A193452 A003451 A013934
Adjacent sequences: A022557 A022558 A022559 * A022561 A022562 A022563
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KEYWORD
| nonn
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AUTHOR
| Andre Kundgen (kundgen(AT)math.uiuc.edu)
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EXTENSIONS
| More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 13 2003
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