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Search: id:A157212
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| A157212 |
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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=3; 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
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| 1, 1, 1, 1, 5, 1, 1, 24, 24, 1, 1, 103, 306, 103, 1, 1, 422, 3028, 3028, 422, 1, 1, 1701, 26064, 57806, 26064, 1701, 1, 1, 6820, 207132, 889640, 889640, 207132, 6820, 1, 1, 27299, 1569298, 11975936, 22436968, 11975936, 1569298, 27299, 1, 1, 109218
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:
1, 2, 7, 50, 514, 6902, 113338, 2207186, 49582036, 1263971354, 36002617324,...
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FORMULA
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Tent function:f(n,m)=If[k <= Floor[n/2], k, n - k]; Recursion:m=2; 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
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{1},
{1, 1},
{1, 5, 1},
{1, 24, 24, 1},
{1, 103, 306, 103, 1},
{1, 422, 3028, 3028, 422, 1},
{1, 1701, 26064, 57806, 26064, 1701, 1},
{1, 6820, 207132, 889640, 889640, 207132, 6820, 1},
{1, 27299, 1569298, 11975936, 22436968, 11975936, 1569298, 27299, 1},
{1, 109218, 11544744, 147711834, 472619880, 472619880, 147711834, 11544744, 109218, 1},
{1, 436897, 83379864, 1716979026, 8806872054, 14787281640, 8806872054, 1716979026, 83379864, 436897, 1}
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MATHEMATICA
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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
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Sequence in context: A080249 A157154 A022168 this_sequence A156600 A152572 A118190
Adjacent sequences: A157209 A157210 A157211 this_sequence A157213 A157214 A157215
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 25 2009
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