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 A258490 Number of words of length 2n such that all letters of the ternary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word. 2
 5, 56, 465, 3509, 25571, 184232, 1325609, 9567545, 69387483, 505915981, 3708195075, 27314663271, 202116910415, 1501769001416, 11200258810265, 83815491037841, 629152465444715, 4735907436066401, 35740538971518155, 270356740041089471, 2049510329494271615 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..1000 FORMULA a(n) ~ 8^n / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jun 01 2015 Conjecture: 4*n*(n-1)*(46829*n-161203)*a(n) -(n-1)*(4865671*n^2-22433759*n+19821114)*a(n-1) +6*(7756949*n^3-53792553*n^2+117956226*n-84118712)*a(n-2) +(-200071007*n^3+1677158106*n^2-4623144589*n+4201946850)*a(n-3) +2*(2*n-7)*(93171685*n^2-585009841*n+881711802)*a(n-4) -72*(2*n-7)*(2*n-9)*(744719*n-1901876)*a(n-5)=0. - R. J. Mathar, Aug 07 2015 EXAMPLE a(3) = 5: aabbcc, aabccb, abbacc, abbcca, abccba. MAPLE A:= proc(n, k) option remember; `if`(n=0, 1, k/n*       add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))     end: T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k): a:= n-> T(n, 3): seq(a(n), n=3..25); MATHEMATICA A[n_, k_] := A[n, k] = If[n == 0, 1, k/n*Sum[Binomial[2*n, j]*(n - j)*If[j == 0, 1, (k - 1)^j], {j, 0, n - 1}]]; T[n_, k_] := Sum[(-1)^i*A[n, k - i]/(i!*(k - i)!), {i, 0, k}]; a[n_] := T[n, 3]; Table[a[n], {n, 3, 25}] (* Jean-François Alcover, May 18 2018, translated from Maple *) CROSSREFS Column k=3 of A256117. Sequence in context: A030060 A247710 A247774 * A255953 A174249 A073563 Adjacent sequences:  A258487 A258488 A258489 * A258491 A258492 A258493 KEYWORD nonn AUTHOR Alois P. Heinz, May 31 2015 STATUS approved

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Last modified November 23 17:10 EST 2020. Contains 338595 sequences. (Running on oeis4.)