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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; text; 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.

LINKS

Table of n, a(n) for n=0..52.

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 A328888

Adjacent sequences:  A157265 A157266 A157267 * A157269 A157270 A157271

KEYWORD

nonn,tabf,uned

AUTHOR

Roger L. Bagula, Feb 26 2009

STATUS

approved

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Last modified August 4 19:54 EDT 2020. Contains 336202 sequences. (Running on oeis4.)