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A026778
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a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026769.
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10
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1, 3, 7, 16, 35, 78, 171, 383, 849, 1919, 4301, 9807, 22193, 50993, 116349, 269094, 618277, 1437916, 3323277, 7764996, 18035275, 42304904, 98668223, 232198092, 543453693, 1282401208, 3010275001, 7119589730, 16753996391
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OFFSET
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0,2
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LINKS
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MAPLE
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T:= proc(n, k) option remember;
if n<0 then 0;
elif k=0 or k=n then 1;
elif n=2 and k=1 then 2;
elif 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, Nov 01 2019
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[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, Nov 01 2019 *)
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PROG
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(Sage)
@CachedFunction
def T(n, k):
if n < 0:
return 0
elif (k==0 or k==n): return 1
elif (n==2 and k==1): return 2
elif (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, Nov 01 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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