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Search: id:A107025
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| A107025 |
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Binomial transform of the expansion of 1/(1-x^5-x^6). |
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+0
1
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| 1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 464, 938, 1808, 3459, 6826, 14198, 30960, 69143, 154433, 340006, 734561, 1561313, 3286129, 6900097, 14542101, 30855957, 65908862, 141395972, 303745077, 651763377, 1395140215, 2978858672
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OFFSET
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0,6
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COMMENT
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In general, the binomial transform of 1/(1-x^r-x^(r+1)) is given by (1-x)^r/((1-x)^(r+1)-x^r), with a(n)=sum{k=0..floor((n+1)/2), binomial(n+k,(r+1)k)}= sum{k=0..floor((r+1)n/r), binomial(k,(r+1)n-r*k)}.
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FORMULA
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G.f.: (1-x)^5/((1-x)^6-x^5); a(n)=6a(n-1)-15a(n-2)+20a(n-3)-15a(n-4)+7a(n-5)-a(n-6); a(n)=sum{k=0..floor((n+1)/2), binomial(n+k, 6k)}; a(n)=sum{k0..floor(6n/5), binomial(k, 6n-5k)}.
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CROSSREFS
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Sequence in context: A150732 A061230 A013559 this_sequence A100477 A011367 A150733
Adjacent sequences: A107022 A107023 A107024 this_sequence A107026 A107027 A107028
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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), May 09 2005
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