OFFSET
2,3
LINKS
A. Blecher, C. Brennan, and A. Knopfmacher, Levels in bargraphs, Ars Math. Contemp., 9, 2015, 297-310.
A. Blecher, C. Brennan, and A. Knopfmacher, Peaks in bargraphs, Trans. Royal Soc. South Africa, 71, No. 1, 2016, 97-103.
M. Bousquet-Mélou and A. Rechnitzer, The site-perimeter of bargraphs, Adv. in Appl. Math. 31 (2003), 86-112.
FORMULA
a(n) = Sum(k*A273344(n,k), k>=0).
G.f. g(z) = (1-z)^2 (1-2z-z^2-sqrt((1-z)(1-3z-z^2-z^3)))/(2 sqrt((1-z)(1-3z-z^2-z^3))).
D-finite with recurrence n*a(n) +2*(-3*n+4)*a(n-1) +(9*n-28)*a(n-2) +2*a(n-3) +(-n+16)*a(n-4) +2*(-n+7)*a(n-5) +(-n+8)*a(n-6)=0. - R. J. Mathar, Jun 02 2016
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]; they have 1, 0, 0, 1, 0 levels, respectively.
MAPLE
g := (1/2)*(1-z)^2*(1-2*z-z^2-sqrt((1-z)*(1-3*z-z^2-z^3)))/sqrt((1-z)*(1-3*z-z^2-z^3)): gser := series(g, z = 0, 45): seq(coeff(gser, z, n), n = 2 .. 42);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 21 2016
STATUS
approved