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A157272 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=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, 7, 1, 1, 20, 20, 1, 1, 47, 155, 47, 1, 1, 102, 753, 753, 102, 1, 1, 213, 3004, 7109, 3004, 213, 1, 1, 436, 10800, 48727, 48727, 10800, 436, 1, 1, 883, 36517, 280736, 551251, 280736, 36517, 883, 1, 1, 1778, 118795, 1454163, 4879214, 4879214 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 9, 42, 251, 1712, 13545, 119928, 1187525, 12907902, 153624005,...}. 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..50.

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, 7, 1},

{1, 20, 20, 1},

{1, 47, 155, 47, 1},

{1, 102, 753, 753, 102, 1},

{1, 213, 3004, 7109, 3004, 213, 1},

{1, 436, 10800, 48727, 48727, 10800, 436, 1},

{1, 883, 36517, 280736, 551251, 280736, 36517, 883, 1},

{1, 1778, 118795, 1454163, 4879214, 4879214, 1454163, 118795, 1778, 1},

{1, 3569, 376802, 7022631, 37101835, 64614329, 37101835, 7022631, 376802, 3569, 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: A154233 A174033 A119727 * A176200 A046739 A056752

Adjacent sequences:  A157269 A157270 A157271 * A157273 A157274 A157275

KEYWORD

nonn,tabf,uned

AUTHOR

Roger L. Bagula, Feb 26 2009

STATUS

approved

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)