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.

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

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).

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

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,easy

Author

Emeric Deutsch and Sergi Elizalde, Jun 27 2016

Status

approved