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 A013986 Expansion of 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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:=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 STATUS approved

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Last modified May 7 00:04 EDT 2021. Contains 343609 sequences. (Running on oeis4.)