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Search: id:A097137
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| A097137 |
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Convolution of 3^n and floor(n/2). |
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+0
1
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| 0, 0, 1, 4, 14, 44, 135, 408, 1228, 3688, 11069, 33212, 99642, 298932, 896803, 2690416, 8071256, 24213776, 72641337, 217924020, 653772070, 1961316220, 5883948671, 17651846024, 52955538084, 158866614264, 476599842805
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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a(n+1) gives partial sums of A033113 and second partial sums of A015518(n+1). Binomial transform of {0,0,1,1,4,4,16,16,....}.
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FORMULA
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G.f. : x^2/((1-x)(1-3x)(1-x^2)); a(n)=sum{k=0..n, floor((n-k)/2)3^k}=sum{k=0..n, floor(k/2)3^(n-k)}; a(n)=4a(n-1)-2a(n-2)-4a(n-3)+3a(n-4).
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CROSSREFS
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Sequence in context: A027831 A097894 A065835 this_sequence A083377 A047115 A125068
Adjacent sequences: A097134 A097135 A097136 this_sequence A097138 A097139 A097140
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KEYWORD
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nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 29 2004
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