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A017875
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Expansion of 1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17).
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1
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1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 10, 13, 15, 18, 22, 27, 33, 40, 49, 61, 74, 89, 108, 131, 159, 193, 235, 288, 352, 428, 521, 634, 771, 937, 1139, 1387, 1690, 2057, 2504, 3049
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OFFSET
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0,17
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COMMENTS
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Number of compositions of n into parts p where 8 <= p <= 17. [Joerg Arndt, Jun 29 2013]
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).
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FORMULA
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a(n) = a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) for n>16. - Vincenzo Librandi, Jun 29 2013
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MATHEMATICA
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CoefficientList[Series[1 / (1 - Total[x^Range[8, 17]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2}, 60] (* Harvey P. Dale, Oct 13 2013 *)
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PROG
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(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2]; [n le 17 select I[n] else Self(n-8)+Self(n-9)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17): n in [1..70]]; // Vincenzo Librandi, Jun 29 2013
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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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