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A025784
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Expansion of 1/((1-x)(1-x^7)(1-x^8)).
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1
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1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42
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OFFSET
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0,8
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COMMENTS
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Number of partitions of n into parts 1, 7, and 8. - Alois P. Heinz, Sep 01 2014
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 1).
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FORMULA
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a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1, a(7)=2, a(8)=3, a(9)=3, a(10)=3, a(11)=3, a(12)=3, a(13)=3, a(14)=4, a(15)=5, a(n)= a(n-1)+ a(n-7)- a(n-9)-a(n-15)+a(n-16). - Harvey P. Dale, Jul 14 2015
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-x^7)(1-x^8)), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 4, 5}, 100] (* Harvey P. Dale, Jul 14 2015 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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