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Search: id:A097979
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| A097979 |
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Total number of largest parts in all compositions of n. |
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+0
2
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| 1, 3, 6, 12, 23, 46, 91, 183, 367, 737, 1478, 2962, 5928, 11858, 23707, 47384, 94698, 189260, 378277, 756160, 1511730, 3022672, 6044472, 12088395, 24177600, 48359695, 96732370, 193495606, 387057584, 774248858, 1548754115, 3097980230
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OFFSET
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1,2
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COMMENT
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Also number of compositions of n+1 with unique largest part. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 03 2005
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FORMULA
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G.f.: (1-x)^2*Sum(x^k/(1-2*x+x^(k+1))^2, k=1..infinity).
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PROGRAM
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(PARI) { b(t)=local(r); sum(k=1, t, forstep(s=t%k, t-k, k, u=(t-k-s)\k; r+=binomial(-2, s)*(-2)^(s-u)*binomial(s, u))); r } { a(n)=b(n)-2*b(n-1)+b(n-2) } (Alekseyev)
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CROSSREFS
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Cf. A097941, A046746.
Sequence in context: A050243 A024505 A005256 this_sequence A003204 A038620 A039695
Adjacent sequences: A097976 A097977 A097978 this_sequence A097980 A097981 A097982
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 07 2004
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EXTENSIONS
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More terms from Max Alekseyev (maxale(AT)gmail.com), Apr 16 2005
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