A143188 A symmetrical triangle sequence with low, even center: t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m].

1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 12, 8, 1, 1, 10, 20, 20, 10, 1, 1, 12, 30, 120, 30, 12, 1, 1, 14, 42, 210, 210, 42, 14, 1, 1, 16, 56, 336, 280, 336, 56, 16, 1, 1, 18, 72, 504, 504, 504, 504, 72, 18, 1, 1, 20, 90, 720, 840, 2520, 840, 720, 90, 20, 1

Offset

1,5

Comments

Row sums are:

{1, 2, 6, 14, 30, 62, 206, 534, 1098, 2198, 5862}.

Links

Table of n, a(n) for n=1..66.

Formula

t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m].

Example

{1},
{1, 1},
{1, 4, 1},
{1, 6, 6, 1},
{1, 8, 12, 8, 1},
{1, 10, 20, 20, 10, 1},
{1, 12, 30, 120, 30, 12, 1},
{1, 14, 42, 210, 210, 42, 14, 1},
{1, 16, 56, 336, 280, 336, 56, 16, 1},
{1, 18, 72, 504, 504, 504, 504, 72, 18, 1},
{1, 20, 90, 720, 840, 2520, 840, 720, 90, 20, 1}

Mathematica

Clear[t, n, m]; t[n_, m_] = If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A159040 A132046 A141540 * A102413 A144480 A144463

Adjacent sequences: A143185 A143186 A143187 * A143189 A143190 A143191

Keyword

nonn,uned

Author

Roger L. Bagula and Gary W. Adamson, Oct 17 2008

Status

approved