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A157207
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Additive 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, 5, 1, 1, 14, 14, 1, 1, 33, 94, 33, 1, 1, 72, 442, 442, 72, 1, 1, 151, 1752, 3818, 1752, 151, 1, 1, 310, 6306, 25358, 25358, 6306, 310, 1, 1, 629, 21390, 144524, 268852, 144524, 21390, 629, 1, 1, 1268, 69822, 746744, 2312836, 2312836, 746744, 69822
(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, 7, 30, 162, 1030, 7626, 63950, 601940, 6261342, 71506072,...
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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, 5, 1},
{1, 14, 14, 1},
{1, 33, 94, 33, 1},
{1, 72, 442, 442, 72, 1},
{1, 151, 1752, 3818, 1752, 151, 1},
{1, 310, 6306, 25358, 25358, 6306, 310, 1},
{1, 629, 21390, 144524, 268852, 144524, 21390, 629, 1},
{1, 1268, 69822, 746744, 2312836, 2312836, 746744, 69822, 1268, 1},
{1, 2547, 222136, 3609722, 17369484, 29098292, 17369484, 3609722, 222136, 2547, 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: A111910 A181143 A144438 * A008957 A136267 A109960
Adjacent sequences: A157204 A157205 A157206 * A157208 A157209 A157210
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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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