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A026539
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a(n) = T(n,n-2), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.
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2
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1, 1, 5, 8, 27, 49, 150, 284, 845, 1625, 4797, 9288, 27377, 53207, 156900, 305720, 902394, 1761882, 5205950, 10181720, 30114073, 58983859, 174609162, 342449340, 1014555607, 1992082339, 5906040623, 11608506392, 34438443075
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OFFSET
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2,3
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LINKS
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FORMULA
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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], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k], T[n-1, k-2] + T[n-1, k]] ]]; Table[T[n, n-2], {n, 2, 35}] (* G. C. Greubel, Apr 10 2022 *)
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PROG
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(SageMath)
@CachedFunction
if k < 0 or n < 0: return 0
elif k == 0 or k == 2*n: return 1
elif k == 1 or k == 2*n-1: return n//2
elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
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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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