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A369809
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Expansion of 1/(1 - x^6/(1-x)^7).
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5
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1, 0, 0, 0, 0, 0, 1, 7, 28, 84, 210, 462, 925, 1730, 3108, 5565, 10388, 20944, 45697, 104673, 242481, 553455, 1229305, 2650221, 5565127, 11465758, 23397041, 47757235, 98317135, 205108561, 433747259, 926655972, 1989584722, 4271185538, 9133958765, 19421679515
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OFFSET
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0,8
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COMMENTS
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Number of compositions of 7*n-6 into parts 6 and 7.
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LINKS
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FORMULA
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a(n) = A017847(7*n-6) = Sum_{k=0..floor((7*n-6)/6)} binomial(k,7*n-6-6*k) for n > 0.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7) for n > 7.
a(n) = Sum_{k=0..floor(n/6)} binomial(n-1+k,n-6*k).
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^6/(1-x)^7))
(PARI) a(n) = sum(k=0, n\6, binomial(n-1+k, n-6*k));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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