A144470 - OEIS

%I #7 Oct 17 2015 16:42:49

%S 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 1,1,21,189,945,945,189,21,1,1,24,252,1512,5670,1512,252,24,1,1,27,

%U 324,2268,10206,10206,2268,324,27,1,1,30,405,3240,17010,61236,17010,3240

%N 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 The row sums are 1, 2, 8, 20, 80, 212, 848, 2312, 9248, 25652, 102608, ...

%F 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 1;

%e 1, 1;

%e 1, 6, 1;

%e 1, 9, 9, 1;

%e 1, 12, 54, 12, 1;

%e 1, 15, 90, 90, 15, 1;

%e 1, 18, 135, 540, 135, 18, 1;

%e 1, 21, 189, 945, 945, 189, 21, 1;

%e 1, 24, 252, 1512, 5670, 1512, 252, 24, 1;

%e 1, 27, 324, 2268, 10206, 10206, 2268, 324, 27, 1;

%e 1, 30, 405, 3240, 17010, 61236, 17010, 3240, 405, 30, 1;

%p 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 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 nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 09 2008