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A026732
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a(n) = Sum_{k=0..n} T(n,k), T given by A026725.
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3
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1, 2, 4, 9, 18, 40, 80, 176, 352, 769, 1538, 3343, 6686, 14477, 28954, 62505, 125010, 269216, 538432, 1157244, 2314488, 4966260, 9932520, 21282622, 42565244, 91096110, 182192220, 389515284, 779030568, 1664015246, 3328030492
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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Conjecture: +(-n+1)*a(n) +2*a(n-1) +3*(3*n-7)*a(n-2) -10*a(n-3) +(-23*n+95)*a(n-4) +6*a(n-5) +(11*n-95)*a(n-6) +2*a(n-7) +4*(n-7)*a(n-8)=0. - R. J. Mathar, Oct 26 2019
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MAPLE
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end proc:
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MATHEMATICA
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T[n_, k_]:= T[n, k]= 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[n, k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Oct 26 2019 *)
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PROG
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(PARI) T(n, k) = 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(k=0, n-1, T(n-1, k)) ) \\ G. C. Greubel, Oct 26 2019
(Sage)
@CachedFunction
def T(n, k):
if (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(T(n, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 26 2019
(GAP)
T:= function(n, k)
if 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-> T(n, k) )); # G. C. Greubel, Oct 26 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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