A152236 A modulo two parity function as a triangle sequence: t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, Binomial[n, m], If[Mod[Binomial[ n, m], 2] == 1 && Binomial[n, m] > 1, 1 + Binomial[n, m], 0]].

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 8, 12, 8, 1, 1, 11, 20, 20, 11, 1, 1, 12, 31, 40, 31, 12, 1, 1, 15, 43, 71, 71, 43, 15, 1, 1, 16, 56, 112, 140, 112, 56, 16, 1, 1, 19, 72, 168, 252, 252, 168, 72, 19, 1, 1, 20, 91, 240, 420, 504, 420, 240, 91, 20, 1

Offset

0,5

Comments

Row sums are: {1, 2, 6, 16, 30, 64, 128, 260, 510, 1024, 2048,...}

Links

Table of n, a(n) for n=0..65.

Formula

t(n,m)=Binomial[n,m]+p(n,m);

p(n,m)=If[Mod[Binomial[n, m], 2] == 0, Binomial[n, m], If[Mod[Binomial[ n, m], 2] == 1 && Binomial[n, m] > 1, 1 + Binomial[n, m], 0]].

Example

{1},
{1, 1},
{1, 4, 1},
{1, 7, 7, 1},
{1, 8, 12, 8, 1},
{1, 11, 20, 20, 11, 1},
{1, 12, 31, 40, 31, 12, 1},
{1, 15, 43, 71, 71, 43, 15, 1},
{1, 16, 56, 112, 140, 112, 56, 16, 1},
{1, 19, 72, 168, 252, 252, 168, 72, 19, 1},
{1, 20, 91, 240, 420, 504, 420, 240, 91, 20, 1}

Mathematica

Clear[p];
p[n_, m_] = If[Mod[Binomial[n, m], 2] == 0, Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 1 + Binomial[n, m], 0]];
Table[Table[Binomial[n, m] + p[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A223489 A016521 A146880 * A296180 A157172 A131060

Adjacent sequences: A152233 A152234 A152235 * A152237 A152238 A152239

Keyword

nonn

Author

Roger L. Bagula, Nov 30 2008

Status

approved