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A026643
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a(n) = A026637(n, floor(n/2)).
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9
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1, 1, 2, 4, 8, 13, 26, 46, 92, 166, 332, 610, 1220, 2269, 4538, 8518, 17036, 32206, 64412, 122464, 244928, 467842, 935684, 1794196, 3588392, 6903352, 13806704, 26635774, 53271548, 103020253, 206040506, 399300166, 798600332
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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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a(n) = (4*a(n-1) + (7*n-9)*a(n-2) + 2*a(n-3) + 4*(n-1)*a(n-4))/(2*(n+1)) with a(0) = a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8. - G. C. Greubel, Jul 01 2024
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MATHEMATICA
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T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[(3*n -1)/2], T[n-1, k-1] + T[n-1, k] ]]; (* A026637 *)
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PROG
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(Magma) [1] cat [n le 4 select 2^(n-1) else (4*Self(n-1) +(7*n-9)*Self(n-2) +2*Self(n-3) +4*(n-1)*Self(n-4))/(2*(n+1)): n in [1..40]]; // G. C. Greubel, Jul 01 2024
(SageMath)
@CachedFunction
if n<5: return (1, 1, 2, 4, 8)[n]
else: return (4*a(n-1) +(7*n-9)*a(n-2) +2*a(n-3) +4*(n-1)*a(n-4))/(2*(n+1))
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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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