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Triangle read by rows: t(n,m)=Binomial[n, m] + If[n > 2, 2*Binomial[n - 2, m - 1], 0]; Mod[If[n > 2, 2*Binomial[n - 2, m - 1], 0],2]=0.
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%I #2 Mar 30 2012 17:34:28

%S 1,1,1,1,2,1,1,5,5,1,1,6,10,6,1,1,7,16,16,7,1,1,8,23,32,23,8,1,1,9,31,

%T 55,55,31,9,1,1,10,40,86,110,86,40,10,1,1,11,50,126,196,196,126,50,11,

%U 1,1,12,61,176,322,392,322,176,61,12

%N Triangle read by rows: t(n,m)=Binomial[n, m] + If[n > 2, 2*Binomial[n - 2, m - 1], 0]; Mod[If[n > 2, 2*Binomial[n - 2, m - 1], 0],2]=0.

%C Row sums are:{1, 2, 4, 12, 24, 48, 96, 192, 384, 768, 1536,...}

%e {1}, {1, 1}, {1, 2, 1}, {1, 5, 5, 1}, {1, 6, 10, 6, 1}, {1, 7, 16, 16, 7, 1}, {1, 8, 23, 32, 23, 8, 1}, {1, 9, 31, 55, 55, 31, 9, 1}, {1, 10, 40, 86, 110, 86, 40, 10, 1}, {1, 11, 50, 126, 196, 196, 126, 50, 11, 1}, {1, 12, 61, 176, 322, 392, 322, 176, 61, 12, 1}

%t Table[Table[Binomial[n, m] + If[n > 2, 2*Binomial[n - 2, m - 1], 0], {m, 0, n}], {n, 0, 10}]; Flatten[%]

%Y A146986, A146987, A028262

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Nov 09 2008