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A017822
Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
1
1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 8, 12, 18, 25, 36, 53, 76, 109, 158, 228, 329, 475, 685, 989, 1428, 2060, 2973, 4292, 6194, 8939, 12902, 18621, 26875, 38788, 55981, 80796, 116611, 168300, 242902, 350574, 505972
OFFSET
0,7
COMMENTS
Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7, 8 and 9. - Ilya Gutkovskiy, May 25 2017
FORMULA
a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) for n>8. - Vincenzo Librandi, Jun 27 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[3, 9]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3, 4}, 50] (* Harvey P. Dale, Feb 04 2015 *)
PROG
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x^3-x^4-x^5-x^6-x^7-x^8-x^9)))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3, 4]; [n le 9 select I[n] else Self(n-3)+Self(n-4)+Self(n-5)+Self(n-6)+Self(n-7)+Self(n-8)+Self(n-9): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013
CROSSREFS
Sequence in context: A332839 A319054 A074964 * A292772 A179042 A222786
KEYWORD
nonn,easy
AUTHOR
STATUS
approved