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 A278133 The sum of the heights of all bargraphs of semiperimeter n (n>=2). 1
 1, 3, 10, 32, 101, 318, 1003, 3173, 10071, 32071, 102453, 328260, 1054620, 3396757, 10965653, 35475159, 114989969, 373400210, 1214529314, 3956450250, 12906762704, 42159475998, 137877383739, 451403471067, 1479329370617, 4852295325254, 15928202158814, 52321416289743, 171966242037941, 565480887258368, 1860228812665716, 6121446895971437 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS A. Blecher, C. Brennan, A. Knopfmacher and H. Prodinger, The height and width of bargraphs, Discrete Applied Math. 180, (2015), 36-44 (see pp. 41-42). FORMULA a(n) = Sum(k*A278132(n,k), k>=0). EXAMPLE a(4)=10; indeed, the bargraphs of semiperimeter 4 correspond to the compositions [3],[1,2],[2,2],[2,1],[1,1,1] and the sum of their heights is 3+2+2+2+1=10. MAPLE x := z: y := z: eq := G(h) = x*(y+G(h))+y*G(h-1)+x*(y+G(h))*G(h-1): ic := G(1) = x*y/(1-x): sol := simplify(rsolve({eq, ic}, G(h))): for j to 17 do g[j] := factor(simplify(rationalize(simplify(subs(h = j, sol))))) end do: H[1] := x*y/(1-x): for j from 2 to 50 do H[j] := factor(g[j]-g[j-1]) end do: for j to 17 do Hser[j] := series(H[j], z = 0, 50) end do: T := proc (n, k) coeff(Hser[k], z, n) end proc: seq(add(k*T(n, k), k = 1 .. n-1), n = 2 .. 45); CROSSREFS Cf. A278132. Sequence in context: A092822 A017935 A134377 * A077826 A292398 A273351 Adjacent sequences:  A278130 A278131 A278132 * A278134 A278135 A278136 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 31 2016 STATUS approved

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Last modified June 20 17:09 EDT 2021. Contains 345178 sequences. (Running on oeis4.)