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A157278 Even only third term general recursion triangle sequence: Tent even function:f(n,k)=If[k <= Floor[n/2], 2*k, 2*(n - k)]; Recursion function: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). 1
1, 1, 1, 1, 14, 1, 1, 69, 69, 1, 1, 292, 1134, 292, 1, 1, 1187, 11686, 11686, 1187, 1, 1, 4770, 100737, 254132, 100737, 4770, 1, 1, 19105, 795723, 4061249, 4061249, 795723, 19105, 1, 1, 76448, 5990296, 55157324, 111691642, 55157324, 5990296, 76448, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 16, 140, 1720, 25748, 465148, 9752156, 234139780, 6311678792,

189254471200,...}.

LINKS

Table of n, a(n) for n=0..45.

FORMULA

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

Recursion function: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, 14, 1},

{1, 69, 69, 1},

{1, 292, 1134, 292, 1},

{1, 1187, 11686, 11686, 1187, 1},

{1, 4770, 100737, 254132, 100737, 4770, 1},

{1, 19105, 795723, 4061249, 4061249, 795723, 19105, 1},

{1, 76448, 5990296, 55157324, 111691642, 55157324, 5990296, 76448, 1},

{1, 305823, 43843188, 679711878, 2431978506, 2431978506, 679711878, 43843188, 305823, 1},

{1, 1223326, 315465267, 7869494244, 45854022036, 81174061452, 45854022036, 7869494244, 315465267, 1223326, 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: A168622 A168293 A157633 * A144441 A157150 A142461

Adjacent sequences:  A157275 A157276 A157277 * A157279 A157280 A157281

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 26 2009

STATUS

approved

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Last modified May 10 02:36 EDT 2021. Contains 343747 sequences. (Running on oeis4.)