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A026757
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a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026747.
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10
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1, 1, 2, 4, 6, 11, 20, 32, 58, 102, 169, 302, 527, 888, 1573, 2741, 4661, 8215, 14316, 24481, 43023, 74998, 128747, 225867, 393838, 678047, 1188201, 2072239, 3575728, 6261248, 10921278, 18879372, 33040083, 57637061
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OFFSET
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0,3
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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], {k, 0, Floor[n/2]}], {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, k) for k in (0..floor(n/2))) 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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