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 A243228 Number of isoscent sequences of length n with exactly two ascents. 2
 3, 25, 128, 525, 1901, 6371, 20291, 62407, 187272, 552104, 1606762, 4631643, 13256644, 37742047, 107025452, 302585780, 853556449, 2403702976, 6760469822, 18995826302, 53336990264, 149680752886, 419883986837, 1177504825907, 3301408010791, 9254726751126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 4..1000 FORMULA Recurrence: (3*n^3 - 43*n^2 + 120*n + 20)*a(n) = (21*n^3 - 289*n^2 + 712*n + 400)*a(n-1) - (51*n^3 - 665*n^2 + 1374*n + 1540)*a(n-2) + 4*(12*n^3 - 145*n^2 + 230*n + 435)*a(n-3) - (9*n^3 - 87*n^2 + 26*n + 280)*a(n-4) - 2*(3*n^3 - 34*n^2 + 43*n + 100)*a(n-5). - Vaclav Kotesovec, Aug 27 2014 a(n) ~ c * d^n, where d = 2.8019377358048382524722... is the root of the equation 1 + 3*d - 4*d^2 + d^3 = 0, c = 0.9786935821895919379992... is the root of the equation 1 - 49*c^2 + 49*c^3 = 0. - Vaclav Kotesovec, Aug 27 2014 G.f.: x^4*(3 - 5*x + x^2)*(1 - x - x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x + 3*x^2 + x^3)) (conjectured). - Colin Barker, May 05 2019 MAPLE b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add( `if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1))) end: a:= n-> coeff(b(n-1, 0\$2), x, 2): seq(a(n), n=4..35); MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n < 1, 1, Expand[Sum[ If[j > i, x, 1] *b[n - 1, j, t + If[j == i, 1, 0]], {j, 0, t + 1}]]]; a[n_] := Coefficient [b[n - 1, 0, 0], x, 2]; Table[a[n], {n, 4, 35}] (* Jean-François Alcover, Feb 09 2015, after Maple *) CROSSREFS Column k=2 of A242351. Sequence in context: A095664 A215773 A099868 * A112495 A034578 A265874 Adjacent sequences: A243225 A243226 A243227 * A243229 A243230 A243231 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Jun 01 2014 STATUS approved

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Last modified March 31 19:11 EDT 2023. Contains 361672 sequences. (Running on oeis4.)