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A157274 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=3; 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, 17, 1, 1, 84, 84, 1, 1, 355, 1431, 355, 1, 1, 1442, 14827, 14827, 1442, 1, 1, 5793, 127860, 326591, 127860, 5793, 1, 1, 23200, 1009338, 5239457, 5239457, 1009338, 23200, 1, 1, 92831, 7593061, 71229038, 145043839, 71229038, 7593061 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 19, 170, 2143, 32540, 593899, 12543992, 302873701, 8200735118,

246775826671,...}. 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..42.

FORMULA

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

Recursion: m=3;

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, 17, 1},

{1, 84, 84, 1},

{1, 355, 1431, 355, 1},

{1, 1442, 14827, 14827, 1442, 1},

{1, 5793, 127860, 326591, 127860, 5793, 1}, {1, 23200, 1009338, 5239457, 5239457, 1009338, 23200, 1},

{1, 92831, 7593061, 71229038, 145043839, 71229038, 7593061, 92831, 1},

{1, 371358, 55541709, 877754637, 3166699854, 3166699854, 877754637, 55541709, 371358, 1},

{1, 1485469, 399468378, 10158918249, 59767620231, 106120842015, 59767620231, 10158918249, 399468378, 1485469, 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: A176203 A103637 A229956 * A218115 A144442 A157151

Adjacent sequences:  A157271 A157272 A157273 * A157275 A157276 A157277

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 26 2009

STATUS

approved

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Last modified September 30 01:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)