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Search: id:A099036
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| 1, 1, 3, 6, 13, 27, 56, 115, 235, 478, 969, 1959, 3952, 7959, 16007, 32158, 64549, 129475, 259560, 520107, 1041811, 2086206, 4176593, 8359951, 16730848, 33479407, 66987471, 134021310, 268117645, 536356683, 1072909784, 2146137379
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OFFSET
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0,3
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COMMENT
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Binomial transform of (-1)^n*Fib(n)+1=(-1)^n*A008346(n).
Number of compositions of n+1 that contain 1 as a part. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 26 2004
Generated from iterates of M * [1,1,1,...], where M = a tridiagonal matrix with [0,1,1,1,...] as the main diagonal, [1,1,1,...] as the superdiagonal and [1,0,0,0,...] as the subdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 05 2009]
Starting with offset 1, generated from iterates of M * [1,1,1,...], M*ANS -> M*ANS,...; where M = = a tridiagonal matrix with (0,1,1,1,...) in the main diagonal, (1,1,1,...) in the superdiagonal and (1,0,0,0,...) in the subdiagonal. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 04 2009]
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FORMULA
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G.f.: (1-x)^2/((1-2x)(1-x-x^2)); a(n)=3a(n-1)-a(n-2)-2a(n-3).
a(n) = A101220(1, 2, n+1) - A101220(1, 2, n). - Ross La Haye (rlahaye(AT)new.rr.com), Aug 05 2005
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CROSSREFS
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Cf. A000045.
Sequence in context: A055143 A092539 A094386 this_sequence A131246 A036886 A052251
Adjacent sequences: A099033 A099034 A099035 this_sequence A099037 A099038 A099039
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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), Sep 23 2004
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EXTENSIONS
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More terms from Ross La Haye (rlahaye(AT)new.rr.com), Aug 05 2005
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