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A228645
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Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=9.
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7
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1, 1, 1, 2, 3, 5, 9, 15, 26, 45, 78, 134, 232, 402, 695, 1205, 2086, 3613, 6259, 10841, 18780, 32531, 56354, 97621, 169111, 292954, 507488, 879136, 1522947, 2638242, 4570298, 7917253, 13715281, 23759370, 41159039, 71300984, 123516755, 213971647, 370669282
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OFFSET
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0,4
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 0, 0, -1, -1, -2, -1, -3, -2, 0, 1, 3, 4, 4, 4, 4, 2, 0, -2, -3, -5, -4, -4, -3, -2, 0, 1, 1, 2, 2, 1, 1, 1).
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FORMULA
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G.f.: -(x^30 +x^29 +x^28 +2*x^27 +2*x^26 +2*x^25 +x^24 +x^23 -x^22 -2*x^21 -2*x^20 -4*x^19 -4*x^18 -3*x^17 -2*x^16 -x^15 +2*x^13 +2*x^12 +3*x^11 +3*x^10 +x^9 +x^8 -x^5 -x^4 -x^3 -x^2+1) / ((x-1)*(x^2 +x+1)*(x^6 +x^3+1)*(x^26 +x^25 +x^24 +2*x^23 +2*x^22 +x^21 +x^20 -2*x^18 -2*x^17 -3*x^16 -3*x^15 -3*x^14 -x^13 -x^12 +x^11 +2*x^10 +2*x^9 +2*x^8 +x^7 +x^6 -x^3 -x^2 -x+1)).
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MAPLE
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a:= n-> coeff(series(-(x^30 +x^29 +x^28 +2*x^27 +2*x^26 +2*x^25 +x^24 +x^23 -x^22 -2*x^21 -2*x^20 -4*x^19 -4*x^18 -3*x^17 -2*x^16 -x^15 +2*x^13 +2*x^12 +3*x^11 +3*x^10 +x^9 +x^8 -x^5 -x^4 -x^3 -x^2+1) / ((x-1)*(x^2 +x+1)*(x^6 +x^3+1)*(x^26 +x^25 +x^24 +2*x^23 +2*x^22 +x^21 +x^20 -2*x^18 -2*x^17 -3*x^16 -3*x^15 -3*x^14 -x^13 -x^12 +x^11 +2*x^10 +2*x^9 +2*x^8 +x^7 +x^6 -x^3 -x^2 -x+1)), x, n+1), x, n): seq(a(n), n=0..50);
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MATHEMATICA
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nMax = 39; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x] &; A228645 = col[9][[1 ;; nMax]] (* Jean-François Alcover, Nov 03 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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