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1, 1, 4, 8, 23, 54, 143, 354, 914, 2306, 5907, 15012, 38368, 97804, 249865, 637834, 1629729, 4163398, 10640753, 27196246, 69526562, 177757762, 454541197, 1162403180, 2972953385, 7604223184, 19451741733, 49761433640, 127308417226
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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Conjecture: n*a(n) -3*(n-1)*a(n-1) -(5*n-6)*a(n-2) +3*(5*n-13)*a(n-3) +2*(4*n-9)*a(n-4) -8*(2*n-9)*a(n-5) = 0. - R. J. Mathar, Jun 23 2013
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
a[n_]:=a[n]= Sum[T[n, k], {k, 0, n}];
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PROG
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(Sage)
@CachedFunction
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n//2)
else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
@CachedFunction
def A026596(n): return sum( T(n, j) for j in (0..n) )
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CROSSREFS
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Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.
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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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