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A274493 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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..36.

M. Bousquet-Mélou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112.

FORMULA

a(n) = A274491(n,0).

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).

EXAMPLE

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.

MAPLE

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);

CROSSREFS

Cf. A082582, A274491.

Sequence in context: A127601 A030038 A030040 * A324770 A075853 A132045

Adjacent sequences:  A274490 A274491 A274492 * A274494 A274495 A274496

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Sergi Elizalde, Jun 27 2016

STATUS

approved

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Last modified June 2 17:02 EDT 2020. Contains 334787 sequences. (Running on oeis4.)