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A157209 Additive tent three term recursion triangle sequence: Tent function:f(n,m)=If[k <= Floor[n/2], k, n - k]; 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, 11, 1, 1, 54, 54, 1, 1, 229, 822, 229, 1, 1, 932, 8368, 8368, 932, 1, 1, 3747, 72066, 174758, 72066, 3747, 1, 1, 15010, 570006, 2759750, 2759750, 570006, 15010, 1, 1, 60065, 4297714, 37366190, 73850596, 37366190, 4297714, 60065, 1, 1, 240288 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

1, 2, 13, 110, 1282, 18602, 326386, 6689534, 157298536, 4166436170,

122909276068,...

LINKS

Table of n, a(n) for n=0..46.

FORMULA

Tent function:f(n,m)=If[k <= Floor[n/2], k, n - k]; 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, 11, 1},

{1, 54, 54, 1},

{1, 229, 822, 229, 1},

{1, 932, 8368, 8368, 932, 1},

{1, 3747, 72066, 174758, 72066, 3747, 1},

{1, 15010, 570006, 2759750, 2759750, 570006, 15010, 1},

{1, 60065, 4297714, 37366190, 73850596, 37366190, 4297714, 60065, 1},

{1, 240288, 31495488, 460448520, 1591033788, 1591033788, 460448520, 31495488, 240288, 1},

{1, 961183, 226836006, 5336065362, 29880355404, 52020840156, 29880355404, 5336065362, 226836006, 961183, 1}

MATHEMATICA

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

f[n_, k_] := If[k <= Floor[n/2], k, 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: A202870 A202872 A144440 * A014469 A157149 A166979

Adjacent sequences:  A157206 A157207 A157208 * A157210 A157211 A157212

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 25 2009

STATUS

approved

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Last modified December 12 07:17 EST 2018. Contains 318053 sequences. (Running on oeis4.)