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A116406
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Expansion of ((1+x-2x^2)+(1+x)sqrt(1-4x^2))/(2(1-4x^2)).
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2
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1, 1, 2, 3, 7, 11, 26, 42, 99, 163, 382, 638, 1486, 2510, 5812, 9908, 22819, 39203, 89846, 155382, 354522, 616666, 1401292, 2449868, 5546382, 9740686, 21977516, 38754732, 87167164, 154276028, 345994216, 614429672, 1374282019, 2448023843
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Interleaving of A114121 and A032443. Row sums of A116405. Binomial transform is A116409.
Appears to be the number of n-digit binary numbers not having more zeros than ones; equivalently, the number of unrestricted Dyck paths of length n not going below the axis. - R. Stephan (ralf(AT)ark.in-berlin.de), Mar 25 2008
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FORMULA
| a(n)=A114121(n/2)*(1+(-1)^n)/2+A032443((n-1)/2)*(1-(-1)^n)/2.
a(n)=sum{k=0..floor(n/2), binomial(n-1,k)}; - Paul Barry (pbarry(AT)wit.ie), Oct 06 2007
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CROSSREFS
| Sequence in context: A121268 A101173 A005246 * A112843 A036651 A049454
Adjacent sequences: A116403 A116404 A116405 * A116407 A116408 A116409
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 13 2006
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