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A274493
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Number of bargraphs of semiperimeter n having no horizontal segments of length 1 (n>=2). By a horizontal segment of length 1 we mean a horizontal step that is not adjacent to any other horizontal step.
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1
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0, 1, 2, 3, 6, 13, 27, 57, 123, 267, 584, 1289, 2864, 6399, 14373, 32435, 73498, 167175, 381551, 873541, 2005622, 4616895, 10653607, 24638263, 57097885, 132575577, 308378460, 718506295, 1676706422, 3918515001, 9170350093, 21488961641, 50417138776, 118425429213, 278476687643
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OFFSET
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2,3
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LINKS
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FORMULA
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G.f.: g(z)=(1-2z+z^2-2z^3-sqrt((1-z)(1-3z+3z^2-5z^3+4z^4-4z^5)))/(2z^2).
D-finite with recurrence (n+2)*a(n) +2*(-2*n-1)*a(n-1) +6*(n-1)*a(n-2) +4*(-2*n+5)*a(n-3) +9*(n-4)*a(n-4) +4*(-2*n+11)*a(n-5) +4*(n-7)*a(n-6)=0. - R. J. Mathar, Jul 22 2022
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EXAMPLE
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a(4)=2 because the 5 (=A082582(4)) bargraphs of semiperimeter 4 correspond to the compositions [1,1,1],[1,2],[2,1],[2,2],[3] and the corresponding pictures give the values 0,2,2,0,1 for the number of horizontal segments of length 1.
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MAPLE
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g:=((1-2*z+z^2-2*z^3-sqrt((1-z)*(1-3*z+3*z^2-5*z^3+4*z^4-4*z^5)))*(1/2))/z^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=2..36);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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