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A017849
Expansion of 1/(1-x^6-x^7-x^8-x^9).
1
1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 3, 4, 3, 2, 2, 3, 6, 10, 12, 12, 11, 10, 13, 21, 31, 40, 45, 45, 46, 55, 75, 105, 137, 161, 176, 191, 221, 281, 372, 478, 579, 665, 749, 869, 1065, 1352, 1710, 2094, 2471, 2862
OFFSET
0,14
COMMENTS
Number of compositions of n into parts p where 6 <= p <= 9. [Joerg Arndt, Jun 27 2013]
FORMULA
a(0)=1, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=1, a(7)=1, a(8)=1; for n>8, a(n) = a(n-6)+a(n-7)+a(n-8)+a(n-9). - Harvey P. Dale, Aug 18 2012
MATHEMATICA
CoefficientList[Series[1/(1 - x^6 - x^7 - x^8 - x^9), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 1, 1, 1}, 60] (* Harvey P. Dale, Aug 18 2012 *)
CoefficientList[Series[1 / (1 - Total[x^Range[6, 9]]), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 27 2013 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^6-x^7-x^8-x^9))); /* or */ I:=[1, 0, 0, 0, 0, 0, 1, 1, 1]; [n le 9 select I[n] else Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9): n in [1..70]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
Sequence in context: A350862 A030340 A122453 * A134536 A214551 A371769
KEYWORD
nonn,easy
AUTHOR
STATUS
approved