A134635 - OEIS

%I #13 Feb 11 2024 18:30:36

%S 1,2,6,18,54,164,508,1610,5222,17308,58484,200948,700348,2470472,

%T 8804024,31648858,114623366,417820972,1531629764,5642508508,

%U 20878731476,77561756152,289156105544,1081466311108,4056621689564,15257327887384,57525469116168,217383333920040,823195469508792,3123379468819600,11872247508521072,45203794091311354

%N Row sums of triangle A134634.

%H Noah Arbesfeld, <a href="https://doi.org/10.1016/j.disc.2013.08.004">Partial permutations avoiding pairs of patterns</a>, Discrete Math., 313 (2013), 2614-2625.

%F Conjecture: (n+1)*a(n) +(-7*n+1)*a(n-1) +2*(7*n-8)*a(n-2) +4*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, May 30 2014

%F a(n) = 2*A000108(n) - A126966(n). - _Mélika Tebni_, Feb 11 2024

%e a(3) = 18 = sum of row 3 terms of triangle A134634: (5 + 4 + 4 + 5).

%p A134635 := n -> 2*binomial(2*n, n)/(n+1) + add(2^k*binomial(2*n-2*k, n-k)/(2*n-2*k-1), k=0..n): seq(A134635(n), n=0..31); # _Mélika Tebni_, Feb 11 2024

%Y Cf. A000108, A126966, A134634.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Nov 04 2007

%E Corrected and extended by _N. J. A. Sloane_, Feb 18 2013