A277999 Sum of distances between leftmost and rightmost peaks in all bargraphs of semiperimeter n.

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

Offset: 1

Author

Arnold Knopfmacher, Nov 08 2016

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A271941, A273720, A273345, A277973.

Programs

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

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).