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 A271941 Number of peaks in all bargraphs having semiperimeter n (n>=2). 4
 1, 2, 5, 13, 36, 105, 317, 979, 3070, 9731, 31090, 99940, 322832, 1047007, 3407017, 11118165, 36370984, 119234791, 391620238, 1288394790, 4244993865, 14005026856, 46260856498, 152974164616, 506355410344, 1677603452621, 5562725698010, 18459595624048, 61301038293810, 203705244194997 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Robert Israel, Table of n, a(n) for n = 2..1880 A. Blecher, C. Brennan, and A. Knopfmacher, Peaks in bargraphs, Trans. Royal Soc. South Africa, 71, No. 1, 2016, 97-103. M. Bousquet-MÃ©lou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112. FORMULA a(n) = Sum_{k>=1} k*A271940(n,k). G.f.: z^2*((1+z^2)*sqrt(1-4z+2z^2+z^4)+1-4z+2z^2+z^4)/(2(1-3z-z^2-z^3)(1-z)^2). (1-n)*a(n)-a(n+1)+(-4-3*n)*a(n+2)+(-2+4*n)*a(n+3)+(-9-3*n)*a(4+n)+(15+4*n)*a(n+5)+(-4-n)*a(n+6)+2 = 0. - Robert Israel, May 20 2016 EXAMPLE a(4)=5 because each of the 5 (=A082582(4)) bargraphs of semiperimeter 4 (corresponding to the compositions [1,1,1],[1,2],[2,1],[2,2],[3]) has only 1 peak. a(6)=36 because among the 35 (=A082582(6)) bargraphs of semiperimeter 6 only the one corresponding to the composition [2,1,2] has 2 peaks; 34*1 + 1* 2 = 36. MAPLE g := (1/2)*z^2*((1+z^2)*sqrt(1-4*z+2*z^2+z^4)+1-4*z+2*z^2+z^4)/((1-z)^2*(1-3*z-z^2-z^3)): gser := series(g, z = 0, 40): seq(coeff(gser, z, n), n = 2 .. 35); CROSSREFS Cf. A082582, A271940. Sequence in context: A154836 A087626 A125094 * A114465 A135310 A135337 Adjacent sequences:  A271938 A271939 A271940 * A271942 A271943 A271944 KEYWORD nonn AUTHOR Emeric Deutsch, May 20 2016 STATUS approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)