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A144470 Triangle t(n,m) read by rows: t(n,m) = binomial(n,m)*3^m if m <= n/2, else t(n,m) = t(n,n-m).

%I A144470 #7 Oct 17 2015 16:42:49
%S A144470 1,1,1,1,6,1,1,9,9,1,1,12,54,12,1,1,15,90,90,15,1,1,18,135,540,135,18,
%T A144470 1,1,21,189,945,945,189,21,1,1,24,252,1512,5670,1512,252,24,1,1,27,
%U A144470 324,2268,10206,10206,2268,324,27,1,1,30,405,3240,17010,61236,17010,3240
%N A144470 Triangle t(n,m) read by rows: t(n,m) = binomial(n,m)*3^m if m <= n/2, else t(n,m) = t(n,n-m).
%C A144470 The row sums are 1, 2, 8, 20, 80, 212, 848, 2312, 9248, 25652, 102608, ...
%F A144470 t(n,m) = binomial(n,m)*3^m if 0 <= m <= n/2, t(n,m) = binomial(n,m)*3^(n-m) if n/2 < m <= n.
%e A144470 1;
%e A144470 1, 1;
%e A144470 1, 6, 1;
%e A144470 1, 9, 9, 1;
%e A144470 1, 12, 54, 12, 1;
%e A144470 1, 15, 90, 90, 15, 1;
%e A144470 1, 18, 135, 540, 135, 18, 1;
%e A144470 1, 21, 189, 945, 945, 189, 21, 1;
%e A144470 1, 24, 252, 1512, 5670, 1512, 252, 24, 1;
%e A144470 1, 27, 324, 2268, 10206, 10206, 2268, 324, 27, 1;
%e A144470 1, 30, 405, 3240, 17010, 61236, 17010, 3240, 405, 30, 1;
%p A144470 A144470 := proc(n,m) if m <= floor(n/2) then binomial(n,m)*3^m ; else procname(n,n-m) ; end if; end proc: # _R. J. Mathar_, Feb 03 2011
%t A144470 f[n_, m_] = If[m <= Floor[n/2], m, n - m]; Table[Table[Binomial[n, m]*3^f[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%K A144470 nonn,tabl,easy
%O A144470 0,5
%A A144470 _Roger L. Bagula_ and _Gary W. Adamson_, Oct 09 2008