|
%I #22 Jun 07 2023 08:42:05
%S 1,3,1,2,5,1,2,6,7,1,2,8,12,9,1,2,10,20,20,11,1,2,12,30,40,30,13,1,2,
%T 14,42,70,70,42,15,1,2,16,56,112,140,112,56,17,1,2,18,72,168,252,252,
%U 168,72,19,1,2,20,90,240,420,504,420,240,90,21,1,2,22,110,330,660,924,924,660,330,110,23,1
%N Table read by rows: 2*A007318(n,m) - A167374(n,m).
%C Row sums = A000079(n+1), n>0.
%C Warning: row sums are not A046055! - _N. J. A. Sloane_, Jul 08 2009
%C Row sums = A151821(n+1), n>=0. - _Alois P. Heinz_, Jul 13 2009
%C A167374 is a modified version of the pair operator A097806 with (1,1,1,...) in the main diagonal and (-1,-1,-1,...) in the subdiagonal.
%H Alois P. Heinz, <a href="/A131127/b131127.txt">Rows n = 0..140, flattened</a>
%e First few rows of the triangle:
%e 1;
%e 3, 1;
%e 2, 5, 1;
%e 2, 6, 7, 1;
%e 2, 8, 12, 9, 1;
%e 2, 10, 20, 20, 11, 1;
%e ...
%p T:= (n, m)-> 2*binomial(n, m) -(-1)^(n+m)*`if`(n=m or n=m+1, 1, 0): seq(seq(T(n,m), m=0..n), n=0..12); # _Alois P. Heinz_, Jul 13 2009
%t T[n_, m_] := 2*Binomial[n, m] - (-1)^(n+m)*If[n == m || n == m+1, 1, 0];
%t Table[Table[T[n, m], {m, 0, n}], {n, 0, 12}] // Flatten (* _Jean-François Alcover_, May 19 2016, translated from Maple *)
%Y Cf. A007318, A097806, A151821, A167374.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Jun 16 2007
%E Edited by _N. J. A. Sloane_ and _R. J. Mathar_, Jul 09 2009
%E Corrected and extended by _Alois P. Heinz_, Jul 13 2009
%E Definition simplified by _Georg Fischer_, Jun 07 2023
|
