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A127358
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a(n)=sum{k=0..n, C(n,floor(k/2))*2^(n-k)}.
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7
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1, 3, 8, 21, 54, 138, 350, 885, 2230, 5610, 14088, 35346, 88596, 221952, 555738, 1391061, 3480870, 8708610, 21783680, 54483510, 136254964, 340729788, 852000828, 2130354786, 5326563004
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is (-1)^n. In general, given r>=0, the sequence given by sum{k=0..n, C(n,floor(k/2))*r^(n-k)} has Hankel transform (1-r)^n. The sequence is the image of the sequence with g.f. (1+x)/(1-2x) under the Chebyshev mapping g(x)->(1/sqrt(1-4x^2))g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108.
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FORMULA
| G.f.: (1/sqrt(1-4x^2))(1+x*c(x^2))/(1-2*x*c(x^2))
a(n)=2*a(n-1)+A054341(n-1). a(n)=Sum_{k, 0<=k<=n}A126075(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
a(n)= Sum_{k, 0<=k<=n} A061554(n,k)*2^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2009]
a(n) is the sum of top row terms of M^n, M = an infinite square production matrix as follows:
2, 1, 0, 0, 0,...
1, 0, 1, 0, 0,...
0, 1, 0, 1, 0,...
0, 0, 1, 0, 1,...
0, 0, 0, 1, 0,...
... - Gary W. Adamson, Sep 07 2011
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EXAMPLE
| a(3) = 21 = (12 + 6 + 2 + 1), where the top row of M^3 = (12, 6, 2, 1).
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CROSSREFS
| Cf. A107430 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 16 2009]
Sequence in context: A030015 A103446 A094723 * A077849 A135473 A190139
Adjacent sequences: A127355 A127356 A127357 * A127359 A127360 A127361
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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