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A278135 Number of horizontal steps in the valleys of all bargraphs having semiperimeter n (n >=2). 1
0, 0, 0, 0, 1, 9, 51, 236, 979, 3805, 14190, 51488, 183333, 644121, 2241127, 7741378, 26593899, 90971184, 310159487, 1054693058, 3578948942, 12124108632, 41015411703, 138597840864, 467913141789, 1578497031981, 5321685955902, 17931990439148, 60397664457791, 203355625940891 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,6

LINKS

Table of n, a(n) for n=2..31.

A. Blecher, C. Brennan, and A. Knopfmacher, Peaks in bargraphs, Trans. Royal Soc. South Africa, 71, No. 1, 2016, 97-103.

FORMULA

G.f.: g(z) = 2z^6/(Q(R + (1-3z+z^2)(1-z)^2*Q)), where Q = sqrt((1-z)(1-3z-z^2-z^3)) and R = 1 - 7z + 17z^2 - 18z^3 + 9z^4 - 3z^5 + z^6.

a(n) = Sum(k*A278134(n,k), k>=0).

EXAMPLE

a(6) = 1 because among the 35 (=A082582(6)) bargraphs of semiperimeter 6 only one has a valley; it corresponds to the composition [2,1,2] and its width is 1.

MAPLE

Q := sqrt((1-z)*(1-3*z-z^2-z^3)): R := 1-7*z+17*z^2-18*z^3+9*z^4-3*z^5+z^6: g := 2*z^6/(Q*(R+(1-3*z+z^2)*(1-z)^2*Q)): gser := series(g, z = 0, 35): seq(coeff(gser, z, j), j = 2 .. 33);

CROSSREFS

Cf. A082582, A273719, A273720, A278134

Sequence in context: A061178 A246178 A213164 * A097789 A080624 A125319

Adjacent sequences:  A278132 A278133 A278134 * A278136 A278137 A278138

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jan 06 2017

STATUS

approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)