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Search: id:A151688
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| A151688 |
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G.f.: Prod_{ n >= 0} (1 + x^(2^n-1) + 2*x^(2^n)). |
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+0
12
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| 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 18, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 96, 34, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 98, 44, 30, 46, 56, 70, 104, 130, 112, 86, 106, 148, 182, 244, 336, 352, 224, 66, 8, 14, 18, 20, 30, 44
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This is essentially the same g.f. as A151550 but with the n=0 term included.
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FORMULA
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a(n) = Sum_{k >= 0} 2^(wt(n+k)-k)*binomial(wt(n+k),k).
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EXAMPLE
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If written as a triangle, begins:
.2;
.4;
.6,6;
.8,14,16,10,
.8,14,18,20,30,44,40,18,
.8,14,18,20,30,44,42,28,30,46,56,70,104,128,96,34,
....
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CROSSREFS
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Equals 2*A152980 = A147646/2.
Equals limit of rows of triangle in A152968.
For generating functions of the form Prod_{k>=c} (1+a*x^(2^k-1)+b*x^2^k)) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694
Cf. A151550, A139251, A139250.
Sequence in context: A023853 A056526 A049066 this_sequence A159276 A056942 A115947
Adjacent sequences: A151685 A151686 A151687 this_sequence A151689 A151690 A151691
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KEYWORD
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nonn,tabf
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), May 02 2009
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 03 2009, Jul 14 2009
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