|
| |
|
|
A157268
|
|
An additive three term general recursion with always even third term: Tent function(even):f(n,m)=If[k <= Floor[n/2], 2^k, 2^(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).
|
|
0
| |
|
|
1, 1, 1, 1, 6, 1, 1, 17, 17, 1, 1, 40, 126, 40, 1, 1, 87, 606, 606, 87, 1, 1, 182, 2413, 5856, 2413, 182, 1, 1, 373, 8679, 40337, 40337, 8679, 373, 1, 1, 756, 29376, 232726, 497066, 232726, 29376, 756, 1, 1, 1523, 95668, 1205968, 4527078, 4527078, 1205968, 95668
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Row sums are:
{1, 2, 8, 36, 208, 1388, 11048, 98780, 1022784, 11660476, 152094648,...}. With an ordinary tent function the third terms adds both even and odd values.
In this case the result is fixed on only adding even third term factors.
|
|
|
FORMULA
| Tent function(even):f(n,m)=If[k <= Floor[n/2], 2^k, 2^(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).
|
|
|
EXAMPLE
| {1},
{1, 1},
{1, 6, 1},
{1, 17, 17, 1},
{1, 40, 126, 40, 1},
{1, 87, 606, 606, 87, 1},
{1, 182, 2413, 5856, 2413, 182, 1},
{1, 373, 8679, 40337, 40337, 8679, 373, 1},
{1, 756, 29376, 232726, 497066, 232726, 29376, 756, 1},
{1, 1523, 95668, 1205968, 4527078, 4527078, 1205968, 95668, 1523, 1},
{1, 3058, 303735, 5824224, 34800782, 70231048, 34800782, 5824224, 303735, 3058, 1}
|
|
|
MATHEMATICA
| Clear[A, f, n, k, m];
f[n_, k_] := If[k <= Floor[n/2], 2^k, 2^(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}];
|
|
|
CROSSREFS
| Sequence in context: A103999 A154985 A157275 * A146959 A157632 A176125
Adjacent sequences: A157265 A157266 A157267 * A157269 A157270 A157271
|
|
|
KEYWORD
| nonn,tabf,uned
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 26 2009
|
| |
|
|
