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A157273 An additive three term general recursion with always even third term: Tent function(odd):f(n,m)=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1; 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). 1
1, 1, 1, 1, 12, 1, 1, 47, 47, 1, 1, 154, 590, 154, 1, 1, 477, 4498, 4498, 477, 1, 1, 1448, 28323, 71232, 28323, 1448, 1, 1, 4363, 162313, 816503, 816503, 162313, 4363, 1, 1, 13110, 882764, 7897486, 15979230, 7897486, 882764, 13110, 1, 1, 39353, 4654100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 14, 96, 900, 9952, 130776, 1966360, 33565952, 638213280, 13425097760,...}. With an ordinary tent function the third terms adds both even and odd values.

In this case the result is fixed on only adding odd third term factors.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

Tent function(odd):f(n,m)=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1;

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, 12, 1},

{1, 47, 47, 1},

{1, 154, 590, 154, 1},

{1, 477, 4498, 4498, 477, 1},

{1, 1448, 28323, 71232, 28323, 1448, 1},

{1, 4363, 162313, 816503, 816503, 162313, 4363, 1},

{1, 13110, 882764, 7897486, 15979230, 7897486, 882764, 13110, 1},

{1, 39353, 4654100, 69030716, 245382470, 245382470, 69030716, 4654100, 39353, 1},

{1, 118084, 24070601, 565385208, 3247996286, 5749957400, 3247996286, 565385208, 24070601, 118084, 1}

MATHEMATICA

Clear[A, f, n, k, m];

f[n_, k_] :=If[k <= Floor[n/2], 2*k + 1, 2*(n - k) + 1;

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: A174039 A174148 A155495 * A168518 A174667 A174672

Adjacent sequences:  A157270 A157271 A157272 * A157274 A157275 A157276

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 26 2009

STATUS

approved

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Last modified September 25 21:48 EDT 2020. Contains 337344 sequences. (Running on oeis4.)