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A029032
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Expansion of 1/((1-x)(1-x^3)(1-x^4)(1-x^5)).
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0
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1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17, 20, 23, 27, 31, 35, 40, 45, 51, 57, 63, 70, 78, 86, 94, 103, 113, 123, 134, 145, 157, 170, 183, 197, 212, 227, 243, 260, 278, 296, 315, 335, 356, 378, 400, 423, 448, 473
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=4, a(6)=5, a(7)=6, a(8)=8, a(9)=10, a(10)=12, a(11)=14, a(12)=17, a(n)=a(n-1)+a(n-3)-a(n-6)- a(n-7)+ a(n-10)+a(n-12)-a (n-13) [From Harvey P. Dale, Jan 04 2012]
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MAPLE
| M := Matrix(13, (i, j)-> if (i=j-1) or (j=1 and member(i, [1, 3, 10, 12])) then 1 elif j=1 and member(i, [6, 7, 13]) then -1 else 0 fi); a := n -> (M^(n))[1, 1]; seq (a(n), n=0..49); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 25 2008
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MATHEMATICA
| CoefficientList[Series[1/((1-x)(1-x^3)(1-x^4)(1-x^5)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, 1, -1}, {1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 17}, 50] (* From Harvey P. Dale, Jan 04 2012 *)
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CROSSREFS
| Sequence in context: A008724 A112402 A056864 * A059809 A121492 A204580
Adjacent sequences: A029029 A029030 A029031 * A029033 A029034 A029035
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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