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A157210
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Subtractive tent three term recursion triangle sequence: Tent function:f(n,m)=If[k <= Floor[n/2], k, n - k]; Recursion:m=1; A(n,k,m)= ( m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) + m*f[n, k]*A(n - 2, k - 1, m).
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1, 1, 1, 1, 3, 1, 1, 8, 8, 1, 1, 19, 42, 19, 1, 1, 42, 186, 186, 42, 1, 1, 89, 730, 1362, 730, 89, 1, 1, 184, 2640, 8540, 8540, 2640, 184, 1, 1, 375, 9030, 47810, 79952, 47810, 9030, 375, 1, 1, 758, 29722, 246530, 652460, 652460, 246530, 29722, 758, 1, 1, 1525, 95238
(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, 18, 82, 458, 3002, 22730, 194384, 1858942, 19610440,...
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FORMULA
| Tent function:f(n,m)=If[k <= Floor[n/2], k, n - k]; Recursion:m=1; A(n,k,m)= ( m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) - m*f[n, k]*A(n - 2, k - 1, m).
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EXAMPLE
| {1},
{1, 1},
{1, 3, 1},
{1, 8, 8, 1},
{1, 19, 42, 19, 1},
{1, 42, 186, 186, 42, 1},
{1, 89, 730, 1362, 730, 89, 1},
{1, 184, 2640, 8540, 8540, 2640, 184, 1},
{1, 375, 9030, 47810, 79952, 47810, 9030, 375, 1},
{1, 758, 29722, 246530, 652460, 652460, 246530, 29722, 758, 1},
{1, 1525, 95238, 1196806, 4796770, 7429760, 4796770, 1196806, 95238, 1525, 1}
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MATHEMATICA
| Clear[A, f, n, k, m];
f[n_, k_] := If[k <= Floor[n/2], k, n - k];
A[n_, 0, m_] := 1; A[n_, n_, m_] := 1;
A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m*k + 1)*A[n - 1, k, m] - m*f[n, k]*A[n - 2, k - 1, m];
Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];
Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]
Table[Table[Sum[A[n, k, m], {k, 0, n}], {n, 0, 10}], {m, 0, 10}];
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CROSSREFS
| Sequence in context: A094816 A097712 A174117 * A034801 A102435 A152570
Adjacent sequences: A157207 A157208 A157209 * A157211 A157212 A157213
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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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