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A100131
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Sum C(n-2k,2k)2^(n-4k), k=0..floor(n/4).
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3
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1, 2, 4, 8, 17, 38, 88, 208, 497, 1194, 2876, 6936, 16737, 40398, 97520, 235424, 568353, 1372114, 3312564, 7997224, 19306993, 46611190, 112529352, 271669872, 655869073, 1583407994, 3822685036, 9228778040, 22280241089, 53789260190
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of 1,1,1,1,2,2,4,4,8,8,... (g.f. (1-x)(1+x)^2/(1-2x^2)).
Row sums of number triangle A108350. - Paul Barry (pbarry(AT)wit.ie), May 31 2005
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-4,0,1).
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FORMULA
| G.f.: (1-2x)/((1-2x)^2-x^4)=(1-2x)/((1-x)^2(1-2x-x^2)); a(n)=4a(n-1)-4a(n-2)+a(n-4); a(n)=((sqrt(2)+1)^(n+1)+(sqrt(2)-1)^(n+1)(-1)^n)/(4sqrt(2))+(n+1)/2; a(n)=sum{k=0..n, (1-k)A000129(n-k+1)}.
a(n)=sUm{k=0..n, sum{j=0..n-k, C(k, j)*C(n-j, k)*mod(j+1, 2)}}; - Paul Barry (pbarry(AT)wit.ie), May 31 2005
(1/2) [Pell(n) + n + 1 ], with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007
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MAPLE
| with(combinat):seq((n+fibonacci(n, 2))/2, n=1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2008
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MATHEMATICA
| CoefficientList[Series[(1-2x)/((1-2x)^2-x^4), {x, 0, 40}], x] (* From Harvey P. Dale, Mar 22 2011 *)
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CROSSREFS
| Cf. A098576, A100132, A100133.
Sequence in context: A193050 A107597 A082499 * A119685 A025276 A006461
Adjacent sequences: A100128 A100129 A100130 * A100132 A100133 A100134
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 06 2004
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