A026762 a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.

1, 4, 16, 66, 279, 1201, 5242, 23133, 103015, 462269, 2088146, 9487405, 43328580, 198798447, 915950385, 4236322720, 19661850045, 91549502656, 427539667095, 2002120576312, 9399659155395, 44234927105888, 208631813215116

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Maple

T:= proc(n, k) option remember;
   if n<0 then 0;
   elif k=0 or k = n then 1;
   elif type(n, 'odd') and k <= (n-1)/2 then
        procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;
   else
       procname(n-1, k-1)+procname(n-1, k) ;
   end if ;
end proc;
seq(T(2*n-1, n-1), n=1..30); # G. C. Greubel, Oct 31 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[OddQ[n] && k<=(n - 1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]; Table[T[2n-1, n-1], {n, 0, 30}] (* G. C. Greubel, Oct 31 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (mod(n, 2)==1 and k<=(n-1)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[T(2*n-1, n-1) for n in (1..30)] # G. C. Greubel, Oct 31 2019

Crossrefs

Cf. A026747, A026758, A026759, A026760, A026761, A026763, A026764, A026765, A026766, A026767, A026768.

Sequence in context: A081915 A307878 A217632 * A277871 A082307 A099782

Adjacent sequences: A026759 A026760 A026761 * A026763 A026764 A026765

Keyword

nonn

Author

Clark Kimberling

Status

approved