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A017895
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Expansion of 1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19).
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1
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 64, 73, 83, 95, 110, 129, 153, 183, 220, 265, 319, 381, 451, 530, 620, 724, 846, 991, 1165, 1375
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OFFSET
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0,22
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COMMENTS
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Number of compositions (ordered partitions) of n into parts 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19. - Ilya Gutkovskiy, May 27 2017
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1).
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FORMULA
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a(n) = a(n-10) +a(n-11) +a(n-12) +a(n-13) +a(n-14) +a(n-15) +a(n-16) +a(n-17) +a(n-18) +a(n-19) for n>18. - Vincenzo Librandi, Jul 01 2013
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MATHEMATICA
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CoefficientList[Series[1 / (1 - Total[x^Range[10, 19]]), {x, 0, 70}], x] (* Vincenzo Librandi Jul 01 2013 *)
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PROG
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(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x^19))); /* or */ [n in [1] cat [11..19] select 1 else n in [2..10] select 0 else Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16)+Self(n-17)+Self(n-18)+Self(n-19): n in [1..70]]; // Vincenzo Librandi, Jul 01 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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