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
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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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 *) -
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
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
Comments