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A157243
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A Narayana based tent function triangular sequence: tent:f(n,m)=If[k <= Floor[n/2], k, n - k]; t(n,m)=Narayana(n*f(n,m),f(n,m))
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0
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1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 336, 10, 1, 1, 15, 825, 825, 15, 1, 1, 21, 1716, 197676, 1716, 21, 1, 1, 28, 3185, 512050, 512050, 3185, 28, 1, 1, 36, 5440, 1163800, 294296640, 1163800, 5440, 36, 1, 1, 45, 8721, 2395575, 778076145, 778076145
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are:
{1, 2, 5, 14, 358, 1682, 201152, 1030528, 296635194, 1560960974, 833226905282,...}.
The fractal that is generated has the desired self-similar form:
a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 128}];
b = Table[If[m <= n, Mod[a[[n]][[m]], 2], 0], {m, 1, Length[a]}, {n, 1, Length[a]}];
ListDensityPlot[b, Mesh -> False, Frame -> False]
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FORMULA
| Tent:f(n,m)=If[k <= Floor[n/2], k, n - k];
t(n,m)=Narayana(n*f(n,m),f(n,m))
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EXAMPLE
| {1},
{1, 1},
{1, 3, 1},
{1, 6, 6, 1},
{1, 10, 336, 10, 1},
{1, 15, 825, 825, 15, 1},
{1, 21, 1716, 197676, 1716, 21, 1},
{1, 28, 3185, 512050, 512050, 3185, 28, 1},
{1, 36, 5440, 1163800, 294296640, 1163800, 5440, 36, 1},
{1, 45, 8721, 2395575, 778076145, 778076145, 2395575, 8721, 45, 1},
{1, 55, 13300, 4562425, 1851013060, 829515727600, 1851013060, 4562425, 13300, 55, 1}
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MATHEMATICA
| Clear[t, n, m, f, A];
f[n_] = Product[k + 1, {k, 0, n}];
A[n_, m_] = Binomial[n, m]*f[n]/(f[m]*f[n - m]);
g[n_, k_] := If[k <= Floor[n/2], k, n - k];
t[n_, m_] = A[n*g[n, m], g[n, m]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A180959 A131235 A202812 * A146769 A189610 A172427
Adjacent sequences: A157240 A157241 A157242 * A157244 A157245 A157246
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 25 2009
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