A013986 Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9).

1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 33, 54, 86, 139, 223, 359, 577, 928, 1492, 2399, 3858, 6203, 9975, 16039, 25791, 41471, 66685, 107228, 172421, 277250, 445813, 716860, 1152698, 1853519, 2980426, 4792474, 7706215

Offset

0,5

Comments

Number of compositions of n into parts p where 2 <= p < = 9. [Joerg Arndt, Jun 24 2013]

Links

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

R. Mullen, On Determining Paint by Numbers Puzzles with Nonunique Solutions, JIS 12 (2009) 09.6.5

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

Formula

a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=3, a(6)=5, a(7)=8, a(8)=13, a(n)=a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9). - Harvey P. Dale, Dec 17 2013

Mathematica

CoefficientList[Series[1 / (1 - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8 - x^9), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2013 *)
CoefficientList[Series[1/(1-Total[x^Range[2, 9]]), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 1, 1, 2, 3, 5, 8, 13}, 40] (* Harvey P. Dale, Dec 17 2013 *)

Prog

(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9))); // Vincenzo Librandi, Jun 24 2013

Crossrefs

See A000045 for the Fibonacci numbers.

Sequence in context: A309676 A280198 A175712 * A121343 A321021 A236768

Adjacent sequences: A013983 A013984 A013985 * A013987 A013988 A013989

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved