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A017866 Expansion of 1/(1-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15-x^16-x^17). 1
1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 5, 6, 7, 9, 12, 16, 21, 25, 30, 36, 44, 55, 70, 90, 113, 140, 172, 211, 261, 325, 408, 512, 640, 796, 986, 1222, 1517, 1889, 2357, 2942, 3668, 4564, 5673, 7050, 8767 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,15
COMMENTS
Number of compositions of n into parts p where 7 <= p <= 17. [Joerg Arndt, Jun 29 2013]
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1).
FORMULA
a(n) = a(n-7) +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 28 2013
MATHEMATICA
CoefficientList[Series[1 / (1 - Total[x^Range[7, 17]]), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4}, 60] (* Harvey P. Dale, May 16 2020 *)
PROG
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^7-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, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4 ]; [n le 17 select I[n] else Self(n-7)+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 28 2013
CROSSREFS
Sequence in context: A291812 A363694 A330292 * A086886 A017840 A017855
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 12 19:05 EDT 2024. Contains 371636 sequences. (Running on oeis4.)