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Search: id:A113405
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| A113405 |
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G.f.: x^3/(1-2x+x^3-2x^4). |
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+0
12
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| 0, 0, 0, 1, 2, 4, 7, 14, 28, 57, 114, 228, 455, 910, 1820, 3641, 7282, 14564, 29127, 58254, 116508, 233017, 466034, 932068, 1864135, 3728270, 7456540, 14913081, 29826162, 59652324, 119304647, 238609294, 477218588, 954437177, 1908874354, 3817748708
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A transform of the Jacobsthal numbers. A059633 is the equivalent transform of the Fibonacci numbers.
Paul Curtz (bpcrtz(AT)free.fr), Aug 05 2007, observes that the inverse binomial transform of 0,0,0,1,2,4,7,14,28,57,114,228,455,910,1820,... gives the same sequence up to signs. That is, the extended sequence is an eigen-sequence for the inverse binomial transform.
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
N. J. A. Sloane, Transforms
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FORMULA
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a(n)=2a(n-1)-a(n-3)+2a(n-4); a(n)=sum{k=0..floor(n/2), C(n-k, k)A001045(k)}; a(n)=sum{k=0..n, C((n+k)/2, k)A001045((n-k)/2)(1+(-1)^(n-k))/2}.
a(3n) = A015565(n), a(3n+1) = 2*A015565(n), a(3n+2) = 4*A015565(n). - Paul Curtz (bpcrtz(AT)free.fr), Nov 30 2007
a(n+1)-2a(n)=hexaperiodic 0, 0, 1, 0, 0, -1, A131531. a(n)+a(n+3)=2^n, A000079. - Paul Curtz (bpcrtz(AT)free.fr), Dec 16 2007
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CROSSREFS
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Adjacent sequences: A113402 A113403 A113404 this_sequence A113406 A113407 A113408
Sequence in context: A018330 A068060 A057744 this_sequence A119340 A119341 A119342
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 28 2005
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EXTENSIONS
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Edited by njas, Dec 13 2007
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