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A083327
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An alternating sum of decreasing powers.
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1
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0, 1, 7, 40, 217, 1156, 6097, 31900, 165697, 855076, 4387537, 22404460, 113945377, 577590196, 2919923377, 14729076220, 74167952257, 372944296516, 1873182473617, 9399885079180, 47135702874337, 236224784974036
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A053154 (with leading zero).
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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a(n)=(5^n-4^n+3^n-2^n)/2 G.f. x(1-7x+13x^2)/((1-2x)(1-3x)(1-4x)(1-5x)) E.g.f. exp(5x)-exp(4x)+exp(3x)-exp(2x)
a(0)=0, a(1)=1, a(2)=7, a(3)=40, a(n)=14*a(n-1)-71*a(n-2)+154*a(n-3)- 120*a(n-4). - Harvey P. Dale, Apr 04 2013
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MATHEMATICA
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Table[(5^n-4^n+3^n-2^n)/2, {n, 0, 30}] (* or *) LinearRecurrence[{14, -71, 154, -120}, {0, 1, 7, 40}, 30] (* Harvey P. Dale, Apr 04 2013 *)
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CROSSREFS
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Cf. A083328.
Sequence in context: A055282 A093737 A081039 * A026716 A026782 A099459
Adjacent sequences: A083324 A083325 A083326 * A083328 A083329 A083330
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Apr 27 2003
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STATUS
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approved
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