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%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
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