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A026754
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a(n) = Sum{k=0..n} T(n,k), T given by A026747.
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11
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1, 2, 5, 10, 24, 48, 114, 228, 540, 1080, 2558, 5116, 12133, 24266, 57658, 115316, 274600, 549200, 1310817, 2621634, 6271788, 12543576, 30076629, 60153258, 144550655, 289101310, 696176322, 1392352644, 3359516328
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listen;
history;
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internal format)
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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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A026747 := proc(n, k) option remember;
if k=0 or k = n then 1;
elif type(n, 'even') and k <= n/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:
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/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 29 2019 *)
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PROG
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(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
elif (mod(n, 2)==0 and k<=n/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 29 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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