A026767 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026758.

1, 3, 7, 16, 34, 75, 157, 345, 721, 1588, 3322, 7342, 15382, 34117, 71587, 159322, 334792, 747507, 1572937, 3522561, 7421809, 16667530, 35158972, 79162689, 167170123, 377291856, 797535322, 1803925336, 3816705364

Offset

0,2

Comments

Partial sums of A026765.

Links

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

Formula

Conjecture: (n+1)*a(n) +(-n-3)*a(n-1) +2*(-5*n+4)*a(n-2) +2*(5*n+3)*a(n-3) +(29*n-83)*a(n-4) +(-29*n+61)*a(n-5) +10*(-2*n+11)*a(n-6) +20*(n-5)*a(n-7)=0. - R. J. Mathar, Jun 30 2013

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( add(add(T(j, k), k=0..n), j=0..n), n=0..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[Sum[T[j, k], {k, 0, n}, {j, 0, n}], {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)
[sum(sum(T(j, k) for k in (0..n)) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 31 2019

Crossrefs

Cf. A026758, A026759, A026760, A026761, A026762, A026763, A026764, A026765, A026766, A026768.

Sequence in context: A238089 A335713 A026734 * A240740 A239257 A268394

Adjacent sequences: A026764 A026765 A026766 * A026768 A026769 A026770

Keyword

nonn

Author

Clark Kimberling

Status

approved