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A174301
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A symmetrical triangle: T(n,k) = binomial(n, k)*if(floor(n/2) greater than or equal to k then 4^k, otherwise 4^(n-k)).
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3
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1, 1, 1, 1, 8, 1, 1, 12, 12, 1, 1, 16, 96, 16, 1, 1, 20, 160, 160, 20, 1, 1, 24, 240, 1280, 240, 24, 1, 1, 28, 336, 2240, 2240, 336, 28, 1, 1, 32, 448, 3584, 17920, 3584, 448, 32, 1, 1, 36, 576, 5376, 32256, 32256, 5376, 576, 36, 1, 1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, 10, 26, 130, 362, 1810, 5210, 26050, 76490, ...}.
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LINKS
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FORMULA
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T(n, m) = binomial(n, m)*if(floor(n/2) greater than or equal to m then 4^m, otherwise 4^(n-m)).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 8, 1;
1, 12, 12, 1;
1, 16, 96, 16, 1;
1, 20, 160, 160, 20, 1;
1, 24, 240, 1280, 240, 24, 1;
1, 28, 336, 2240, 2240, 336, 28, 1;
1, 32, 448, 3584, 17920, 3584, 448, 32, 1;
1, 36, 576, 5376, 32256, 32256, 5376, 576, 36, 1;
1, 40, 720, 7680, 53760, 258048, 53760, 7680, 720, 40, 1;
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MATHEMATICA
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Table[Binomial[n, m]*If[Floor[n/2]>=m , 4^m, 4^(n-m)], {n, 0, 10}, {m, 0, n} ]//Flatten
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PROG
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(PARI) {T(n, k) = binomial(n, k)*if(floor(n/2)>=k, 4^k, 4^(n-k))}; \\ G. C. Greubel, Apr 15 2019
(Magma) [[Floor(n/2) ge k select 4^k*Binomial(n, k) else 4^(n-k)*Binomial(n, k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Apr 15 2019
(Sage)
def T(n, k):
if floor(n/2)>=k: return 4^k*binomial(n, k)
else: return 4^(n-k)*binomial(n, k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Apr 15 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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