The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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]]. 0

%I #2 Mar 30 2012 17:34:28

%S 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,

%T 15,43,71,71,43,15,1,1,16,56,112,140,112,56,16,1,1,19,72,168,252,252,

%U 168,72,19,1,1,20,91,240,420,504,420,240,91,20,1

%N 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]].

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

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

%F 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]].

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 7, 7, 1},

%e {1, 8, 12, 8, 1},

%e {1, 11, 20, 20, 11, 1},

%e {1, 12, 31, 40, 31, 12, 1},

%e {1, 15, 43, 71, 71, 43, 15, 1},

%e {1, 16, 56, 112, 140, 112, 56, 16, 1},

%e {1, 19, 72, 168, 252, 252, 168, 72, 19, 1},

%e {1, 20, 91, 240, 420, 504, 420, 240, 91, 20, 1}

%t Clear[p];

%t 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]];

%t Table[Table[Binomial[n, m] + p[n, m], {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%K nonn

%O 0,5

%A _Roger L. Bagula_, Nov 30 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 19 16:34 EDT 2024. Contains 376014 sequences. (Running on oeis4.)