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%I #13 Dec 29 2023 10:31:08
%S 1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,1,2,3,3,2,1,1,2,4,7,4,2,1,1,3,8,12,12,
%T 8,3,1,1,3,8,20,15,20,8,3,1,1,5,14,45,52,52,45,14,5,1,1,5,26,66,109,
%U 170,109,66,26,5,1
%N Triangle t(n,m) = round(A006720(n)/(A006720(n-m)*A006720(m))) read by rows, 0 <= m <= n.
%C The round-function in the definition is round-to-nearest, not Mathematica's round-to-even. - _R. J. Mathar_, Jul 12 2012
%C Row sums are 1, 2, 3, 4, 8, 12, 21, 48, 79, 234, 584.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 1, 1, 1;
%e 1, 2, 2, 2, 1;
%e 1, 2, 3, 3, 2, 1;
%e 1, 2, 4, 7, 4, 2, 1;
%e 1, 3, 8, 12, 12, 8, 3, 1;
%e 1, 3, 8, 20, 15, 20, 8, 3, 1;
%e 1, 5, 14, 45, 52, 52, 45, 14, 5, 1;
%e 1, 5, 26, 66, 109, 170, 109, 66, 26, 5, 1;
%p A141604 := proc(n,m)
%p round(A006720(n)/A006720(n-m)/A006720(m)) ;
%p end proc:
%p seq(seq(A141604(n,k),k=0..n),n=0..12) ; # _R. J. Mathar_, Jul 12 2012
%t Clear[a, t] (*A006720*) (* _Robert G. Wilson v_, Jul 04 2007 *) a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = (a[n - 1] a[n - 3] + a[n - 2]^2)/a[n - 4]; Array[a, 23]; t[n_, m_] := a[n]/(a[n - m]*a[m]) Table[Table[Round[t[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%Y Cf. A006720.
%K nonn,less,tabl
%O 0,12
%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 21 2008
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