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A277999 Sum of distances between leftmost and rightmost peaks in all bargraphs of semiperimeter n. 0
0, 0, 0, 0, 0, 1, 9, 53, 261, 1165, 4887, 19642, 76519, 291095, 1086946, 3998430, 14530223, 52272218, 186467253, 660449671, 2325124444, 8143334776, 28393762841, 98621419068, 341403900888, 1178425064256, 4057244213071, 13937739553781, 47786215201214, 163554669548711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..30.

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

FORMULA

G.f.: -(4*x^6*(3-2*x^3+3*x^4 - sqx + x^2*(4-3*sqx) + 2*x*(sqx - 4))/((x^2-3*x+1)*sqx*(-1+2*x+x^2-sqx)^3)) where sqx = sqrt(x^4+2*x^2-4*x+1).

EXAMPLE

a(6)=1 since the bargraph with column heights 2,1,2 has a distance of 1 between first and last peak. All other bargraphs of semiperimeter 6 have at most one peak, hence 0 difference.

PROG

(PARI) my(x = 'x + O('x^30)); sqx = sqrt(x^4+2*x^2-4*x+1); concat(vector(5), Vec(-(4*x^6*(3-2*x^3+3*x^4 - sqx + x^2*(4-3*sqx) + 2*x*(sqx - 4))/((x^2-3*x+1)*sqx*(-1+2*x+x^2-sqx)^3)))) \\ Michel Marcus, Feb 25 2019

CROSSREFS

Cf. A271941, A273720, A273345, A277973.

Sequence in context: A202514 A005025 A122588 * A295203 A334977 A038761

Adjacent sequences:  A277996 A277997 A277998 * A278000 A278001 A278002

KEYWORD

nonn

AUTHOR

Arnold Knopfmacher, Nov 08 2016

STATUS

approved

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Last modified October 17 06:40 EDT 2021. Contains 348048 sequences. (Running on oeis4.)