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A094930 Triangle T(n,m) read by rows, defined by squaring a matrix with row entries 2+3*(m-1).

%I A094930 #14 May 06 2019 12:04:47
%S A094930 4,14,25,30,65,64,52,120,152,121,80,190,264,275,196,114,275,400,462,
%T A094930 434,289,154,375,560,682,714,629,400,200,490,744,935,1036,1020,860,
%U A094930 529,252,620,952,1221,1400,1462,1380,1127,676,310,765,1184,1540,1806,1955,1960
%N A094930 Triangle T(n,m) read by rows, defined by squaring a matrix with row entries 2+3*(m-1).
%C A094930 Matrix square of the matrix B(n,m) = 2+3*(m-1), B containing the first terms of A016789
%C A094930 in its row n, n>0, 1<=m<=n.
%H A094930 Robert Israel, <a href="/A094930/b094930.txt">Table of n, a(n) for n = 1..10011</a> (rows 1 to 141, flattened)
%F A094930 T(n,m) = sum_{k=m..n} B(n,k)*B(k,m) = (3*m-1)*(3*m+3*n-2)*(n+1-m)/2.
%F A094930 Row sums: sum_{m=1..n} T(n,m) = A024212(n).
%F A094930 G.f. as triangle: x*y*(4+2*x+13*x*y-16*x^2*y+x^2*y^2-4*x^3*y^2)/((1-x)*(1-x*y))^3. - _Robert Israel_, May 06 2019
%e A094930 The matrix B starts as
%e A094930   2 ;
%e A094930   2,5 ;
%e A094930   2,5,8 ;
%e A094930   2,5,8,11 ;
%e A094930   2,5,8,11,14 ;
%e A094930 and interpreting this as a lower triangular matrix, its square T = B^2 starts
%e A094930   4;
%e A094930   14,25;
%e A094930   30,65,64;
%e A094930   52,120,152,121;
%p A094930 A094930 := proc(n,m) (3*m-1)*(3*m+3*n-2)*(n+1-m)/2 ; end: seq(seq(A094930(n,m),m=1..n),n=1..20) ; # _R. J. Mathar_, Oct 09 2009
%Y A094930 Cf. A024212, A096037, A011379, A002411, A096038, A095794.
%K A094930 nonn,easy,tabl
%O A094930 1,1
%A A094930 _Gary W. Adamson_, Jun 17 2004
%E A094930 Edited and extended by _R. J. Mathar_, Oct 09 2009