A226013 Number of unimodal functions f:[n]->[2n] with f(1)<>1 and f(i)<>f(i+1).

1, 1, 9, 70, 581, 4956, 43065, 379093, 3369301, 30168268, 271716644, 2459014504, 22342432139, 203682343840, 1862165051700, 17066961406095, 156758478514005, 1442549386731900, 13297258924349292, 122757267172891048, 1134800963513922996, 10503230892143398192

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..500

Formula

a(n) ~ 2^(8*n-3/2) / (7*sqrt(Pi*n)*3^(3*n-3/2)). - Vaclav Kotesovec, Jul 16 2014

Recurrence (of order 2): 6*n*(3*n - 4)*(3*n - 2)*(77*n^2 - 244*n + 191)*a(n) = (37345*n^5 - 212742*n^4 + 463115*n^3 - 476646*n^2 + 228792*n - 40320)*a(n-1) + 8*(2*n - 3)*(4*n - 7)*(4*n - 5)*(77*n^2 - 90*n + 24)*a(n-2). - Vaclav Kotesovec, Jul 16 2014

Example

a(0) = 1: [].
a(1) = 1: [2].
a(2) = 9: [2,1], [2,3], [2,4], [3,1], [3,2], [3,4], [4,1], [4,2], [4,3].
a(3) = 70: [2,3,1], [2,3,2], [2,3,4], ..., [6,5,2], [6,5,3], [6,5,4].
a(4) = 581: [2,3,2,1], [2,3,4,1], [2,3,4,2], ..., [8,7,6,3], [8,7,6,4], [8,7,6,5].

Maple

a:= proc(n) option remember; `if`(n<3, (2*n-1)^2,
     ((49421666742*n^4 -205832874348*n^3 +295740702162*n^2
       -167673767628*n +29628103680) *a(n-1)
      +(27981954763*n^4 -127816385262*n^3 +231525900473*n^2
       -221063690262*n +102518080560) *a(n-2)
      +29529976*(2*n-5)*(4*n-9)*(n-3)*(4*n-11) *a(n-3))
      / (288*n*(2131486*n-3539195)*(3*n-4)*(3*n-2)))
    end:
seq(a(n), n=0..30);

Crossrefs

Cf. A014301 (functions f:[n]->[n] with f(1)<>1 and f(i)<>f(i+1)).

Sequence in context: A045739 A098205 A000899 * A156705 A231419 A227848

Adjacent sequences: A226010 A226011 A226012 * A226014 A226015 A226016

Keyword

nonn

Author

Alois P. Heinz, May 22 2013

Status

approved