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A086461 Symmetric version of square array A086460.

%I A086461 #9 Aug 09 2025 20:28:25
%S A086461 1,1,1,1,1,1,1,2,2,1,1,3,4,3,1,1,4,6,6,4,1,1,5,8,9,8,5,1,1,6,10,12,12,
%T A086461 10,6,1,1,7,12,15,16,15,12,7,1,1,8,14,18,20,20,18,14,8,1,1,9,16,21,24,
%U A086461 25,24,21,16,9,1,1,10,18,24,28,30,30,28,24,18,10,1,1,11,20,27,32,35,36
%N A086461 Symmetric version of square array A086460.
%C A086461 Rows include A028310, A004277, A008486, A008574, A008706, A008458. Main diagonal is n^2+0^n (A000290, preceded by extra 1).
%F A086461 T(0, k)=T(n, 0)=1, T(n, k)=nk+0^n, n, k>0
%F A086461 Alternatively, triangle read by rows with formula t(n,m)=If[n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]. - _Roger L. Bagula_, Sep 06 2008
%e A086461 Rows begin
%e A086461   1 1 1 1 1 ...
%e A086461   1 1 2 3 4 ...
%e A086461   1 2 4 6 8 ...
%e A086461   1 3 6 9 12 ...
%e A086461   1 4 8 12 16 ...
%e A086461 As a triangle:
%e A086461   {1},
%e A086461   {1, 1},
%e A086461   {1, 1, 1},
%e A086461   {1, 2, 2, 1},
%e A086461   {1, 3, 4, 3, 1},
%e A086461   {1, 4, 6, 6, 4, 1},
%e A086461   {1, 5, 8, 9, 8, 5, 1},
%e A086461   {1, 6, 10, 12, 12, 10, 6, 1},
%e A086461   {1, 7, 12, 15, 16, 15, 12, 7, 1},
%e A086461   {1, 8, 14, 18, 20, 20, 18, 14, 8, 1},
%e A086461   {1, 9, 16, 21, 24, 25, 24, 21, 16, 9, 1}
%t A086461 t[n_, m_] = If[ n == 0 || n == m || m == 0, 1, n - m]*If[n == m || n == 0 || m == 0, 1, m]; Table[t[n, m], {n, 0, 11}, {m, 0, n}] // Flatten (* _Roger L. Bagula_, Sep 06 2008 *)
%K A086461 easy,nonn,tabl
%O A086461 0,8
%A A086461 _Paul Barry_, Jul 21 2003