A017826 Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13).

1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 40, 59, 87, 126, 184, 270, 394, 575, 841, 1229, 1795, 2623, 3833, 5600, 8183, 11957, 17470, 25527, 37300, 54500, 79633, 116358, 170017, 248421, 362984, 530378, 774966

Offset

0,7

Comments

Number of compositions (ordered partitions) of n into parts 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13. - Ilya Gutkovskiy, May 25 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,1,1,1,1,1,1,1,1).

Formula

a(n) = a(n-3) +a(n-4) +a(n-5) +a(n-6) +a(n-7) +a(n-8) +a(n-9) +a(n-10) +a(n-11) +a(n-12) +a(n-13) for n>12. - Vincenzo Librandi, Jun 27 2013

Mathematica

CoefficientList[Series[1 / (1 - Total[x^Range[3, 13]]), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 27 2013 *)
LinearRecurrence[{0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19}, 50] (* Harvey P. Dale, May 26 2018 *)

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-x^10-x^11-x^12-x^13)))); /* or */ I:=[1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19]; [n le 13 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)+Self(n-10)+Self(n-11)+Self(n-12)+Self(n-13): n in [1..50]]; // Vincenzo Librandi, Jun 27 2013

Crossrefs

Sequence in context: A017825 A247083 A159848 * A068921 A000930 A078012

Adjacent sequences: A017823 A017824 A017825 * A017827 A017828 A017829

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved