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A026537
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a(n) = T(n,n), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n)=0.
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3
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1, 0, 2, 2, 8, 12, 38, 66, 196, 360, 1052, 1980, 5774, 11004, 32146, 61726, 180772, 348912, 1024256, 1984608, 5837908, 11346280, 33433996, 65143716, 192239854, 375351288, 1109049320, 2169299288, 6416509142, 12569973108
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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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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], {n, 0, 35}] (* G. C. Greubel, Apr 10 2022 *)
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PROG
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(SageMath)
@cached_function
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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