A026734 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026725.

1, 3, 7, 16, 34, 74, 154, 330, 682, 1451, 2989, 6332, 13018, 27495, 56449, 118954, 243964, 513180, 1051612, 2208856, 4523344, 9489604, 19422124, 40704746, 83269990, 174366100, 356558320, 746073604, 1525104172, 3189119418

Offset

0,2

Links

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

Maple

A026725:= proc(n, k) option remember;
    if n<0 or k<0 then 0;
    elif k=0 or k=n then 1;
    elif 2*k = n-1 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) ;
fi; end proc:seq(add(add(A026725(i, j), j=0..n), i=0..n), n=0..30); # G. C. Greubel, Oct 26 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[Sum[T[j, k], {k, 0, n}, {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Oct 26 2019 *)

Prog

(PARI) T(n, k) = if(n<0, 0, if(k==n || k==0, 1, if(2*k==n-1, T(n-1, k-1) + T(n-2, k-1) + T(n-1, k), T(n-1, k-1) + T(n-1, k) )));
vector(31, n, sum(j=0, n-1, sum(i=0, n-1, T(j, i))) ) \\ G. C. Greubel, Oct 26 2019
(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-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)
[sum( sum( T(j, k) for k in (0..n)) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 26 2019
(GAP)
T:= function(n, k)
    if n<0 then return 0;
    elif k=0 or k=n then return 1;
    elif 2*k=n-1 then 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);
    fi;
  end;
List([0..30], n-> Sum([0..n], k-> Sum([0..n], j-> T(j, k) )))); # G. C. Greubel, Oct 26 2019

Crossrefs

Partial sums of A026732.

Sequence in context: A281811 A238089 A335713 * A026767 A240740 A239257

Adjacent sequences: A026731 A026732 A026733 * A026735 A026736 A026737

Keyword

nonn

Author

Clark Kimberling

Status

approved