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 A241872 Number of ascent sequences of length n with exactly two descents. 2
 4, 53, 429, 2748, 15342, 78339, 376159, 1728458, 7689744, 33393393, 142376385, 598555320, 2489143090, 10264270175, 42048021027, 171366151974, 695585112660, 2814484154445, 11359684937605, 45759869226260, 184050366838134, 739376299832763, 2967455421451239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 LINKS Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 5..1000 Index entries for linear recurrences with constant coefficients, signature (17,-121,467,-1054,1388,-984,288). FORMULA G.f.: -(12*x^2-15*x+4)*x^5/((4*x-1)*(x-1)*(3*x-1)^2*(2*x-1)^3). a(n) = 4^n/6 - 3^(n-1)*(2*n+1)/4 + 2^(n-4)*(n+2)*(n-1) + 1/12. - Vaclav Kotesovec, May 03 2014 Recurrence: a(n) = 288*a(n-7) - 984*a(n-6) + 1388*a(n-5) - 1054*a(n-4) + 467*a(n-3) - 121*a(n-2) + 17*a(n-1). - Fung Lam, May 05 2014 MAPLE gf := -(12*x^2-15*x+4)*x^5/((4*x-1)*(x-1)*(3*x-1)^2*(2*x-1)^3): a:= n-> coeff(series(gf, x, n+1), x, n): seq(a(n), n=5..30); MATHEMATICA CoefficientList[Series[-(12 x^2 - 15 x + 4)/((4 x - 1) (x - 1) (3 x - 1)^2 (2 x - 1)^3), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2014 *) LinearRecurrence[{17, -121, 467, -1054, 1388, -984, 288}, {4, 53, 429, 2748, 15342, 78339, 376159}, 23] (* Ray Chandler, Jul 14 2015 *) CROSSREFS Column k=2 of A238858. Sequence in context: A219160 A111034 A214367 * A109801 A099340 A221605 Adjacent sequences: A241869 A241870 A241871 * A241873 A241874 A241875 KEYWORD nonn,easy AUTHOR Joerg Arndt and Alois P. Heinz, Apr 30 2014 STATUS approved

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)