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Search: id:A079662
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| A079662 |
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a(n) = the number of occurrences of 1 in all compositions of n without 2's = # of occurrences of the integer k in compositions of n+k-1 without 2's (k > 2). |
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+0
1
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| 1, 2, 3, 6, 13, 26, 50, 96, 184, 350, 661, 1242, 2324, 4332, 8047, 14902, 27521, 50700, 93191, 170942, 312974, 572030, 1043852, 1902044, 3461067, 6289972, 11417576, 20702328, 37498589, 67856074, 122677727, 221599538, 399962369, 721333090
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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P. Chinn and S. Heubach, The Akiyama-Tanigawa algorithm for Bernoulli numbers, J. Integer Sequences, 6 (2003), no. 2, Article 03.2.3.
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FORMULA
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a(n) = c(0)c(n-1) + c(1)c(n-2) + c(2)c(n-3) + ... + c(n-1)c(0), where c(i) is given by sequence A005251; generating function = (x(1-x)^2)/(1-2x+x^2-x^3)^2
a(n) = Sum_{k=1..floor((n+2)/3)} k*binomial(n-k+1, 2*k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2004
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EXAMPLE
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a(4)=6 since the compositions of 4 that do not contain a 2 are 1+1+1+1, 1+3, 3+1 and 4, for a total of 6 1's. Also there are 6 occurrences of 5 in the compositions of 8 (= 4+5-1): 1+1+1+5, 1+1+5+1, 1+5+1+1, 5+1+1+1, 5+3 and 3+5 (only compositions without 2's that contain a 5 are listed).
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MATHEMATICA
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Rest[CoefficientList[ Normal[Series[x(1 - x)^2/((1 - 2x + x^2 - x^3)^2), {x, 0, 50}]], x]]
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CROSSREFS
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Cf. A005251.
Sequence in context: A018274 A018775 A086514 this_sequence A007910 A052702 A058766
Adjacent sequences: A079659 A079660 A079661 this_sequence A079663 A079664 A079665
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KEYWORD
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easy,nonn
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AUTHOR
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Silvia Heubach (sheubac(AT)calstatela.edu), Jan 23 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 24 2003
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