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Search: id:A027934
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| A027934 |
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a(0)=0, a(1)=1, a(3)=2; for n>3, a(n)=3*a(n-1)-a(n-2)-2*a(n-3). |
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13
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| 0, 1, 2, 5, 11, 24, 51, 107, 222, 457, 935, 1904, 3863, 7815, 15774, 31781, 63939, 128488, 257963, 517523, 1037630, 2079441, 4165647, 8342240, 16702191, 33433039, 66912446, 133899917, 267921227, 536038872, 1072395555, 2145305339
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of compositions of n with at least one even part (offset 2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 29 2004
First differences of A008466. a(n) = A008466(n+2) - A008466(n+1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 06 2006
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FORMULA
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a(n)=sum(sum(binomial(n-j, n-2j-k), k, 0, n-2j), j, 0, floor(n/2)) - Paul Barry (pbarry(AT)wit.ie), Feb 07 2003
Row sums of A091597. G.f.: x(1-x)/((1-2x)(1-x-x^2)); a(n)=2^(n+1)-Fib(n+2). - Paul Barry (pbarry(AT)wit.ie), Jan 23 2004
a(n)=sum{j=0..n, sum{k=0..n, binomial(n-k, k+j)}} - Paul Barry (pbarry(AT)wit.ie), Aug 29 2004
a(n) = (sum of (n+1)-th row of the triangle in A108617) / 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 12 2005
a(n) = 2^(n+1)-Fibonacci(n+2). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 06 2006
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CROSSREFS
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Row sums of triangle A131767. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 13 2007
a(n) = A101220(1,2,n+1).
T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027926.
Diagonal sums of A055248
Cf. A000045, A000079, A008466, A059570, A099036, A047967.
Adjacent sequences: A027931 A027932 A027933 this_sequence A027935 A027936 A027937
Sequence in context: A059776 A091360 A090764 this_sequence A134389 A111297 A077864
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Simpler definition from Miklos Kristof (kristmikl(AT)freemail.hu), Nov 24 2003
Initial zero added by njas, Feb 13 2008
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