A026756 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747.

1, 3, 8, 18, 42, 90, 204, 432, 972, 2052, 4610, 9726, 21859, 46125, 103783, 219099, 493699, 1042899, 2353716, 4975350, 11247138, 23790714, 53867343, 114020601, 258571256, 547672566, 1243848888, 2636201532, 5995717860

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Maple

A026747 := proc(n, k) option remember;
   if n<0 then 0;
   elif k=0 or k = n then 1;
   elif type(n, 'even') and k <= n/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(add(add(A026747(i, j), j=0..n), i=0..n), n=0..30); # G. C. Greubel, Oct 29 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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[Sum[T[i, j], {i, 0, n}, {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Oct 29 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)==0 and k<=n/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)
[sum(sum(T(i, j) for j in (0..n)) for i in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 29 2019

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026757.

Sequence in context: A026679 A371682 A191524 * A341583 A216631 A026384

Adjacent sequences: A026753 A026754 A026755 * A026757 A026758 A026759

Keyword

nonn

Author

Clark Kimberling

Status

approved