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A017892
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Expansion of 1/(1 - x^10 - x^11 - x^12 - x^13 - x^14 - x^15 - x^16).
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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, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 4, 5, 7, 10, 15, 21, 28, 33, 36, 37, 37, 37, 38, 41, 50, 66, 90, 119, 150, 180, 207, 229, 246, 259, 276, 306, 359, 441, 554, 696, 862
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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 and 16. - 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).
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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(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=1, a(11)=1, a(12)=1, a(13)=1, a(14)=1, a(15)=1. - Harvey P. Dale, Mar 04 2013
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MAPLE
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a[0]:= 1:
for i from 1 to 9 do a[i]:= 0 od:
for i from 10 to 15 do a[i]:= 1 od:
for i from 16 to 1000 do a[i]:= add(a[j], j=i-16 .. i-10) od:
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MATHEMATICA
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CoefficientList[Series[1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16), {x, 0, 60}], x]
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1}, 70] (* End *)
CoefficientList[Series[1 / (1 - Total[x^Range[10, 16]]), {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))); /* or */ I:=[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]; [n le 16 select I[n] else Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13)+Self(n-14)+Self(n-15)+Self(n-16): n in [1..70]]; // Vincenzo Librandi, Jul 01 2013
(PARI) x='x+O('x^66); Vec(1/(1-x^10-x^11-x^12-x^13-x^14-x^15-x^16)) \\ Altug Alkan, Oct 04 2018
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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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