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A026538
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a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.
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2
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1, 1, 3, 6, 13, 33, 65, 180, 346, 990, 1897, 5502, 10571, 30863, 59523, 174456, 337672, 992304, 1926650, 5673140, 11043858, 32571858, 63548069, 187675644, 366849016, 1084649644, 2123604927, 6284986554, 12322549765, 36501029265
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OFFSET
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1,3
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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-1], {n, 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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