|
%I #9 Aug 17 2022 16:20:54
%S 1,1,1,1,3,1,1,5,3,1,1,7,8,3,1,1,9,16,8,3,1,1,11,27,20,8,3,1,1,13,41,
%T 43,20,8,3,1,1,15,58,81,48,20,8,3,1,1,17,78,138,106,48,20,8,3,1,1,19,
%U 101,218,213,112,48,20,8,3,1
%N Antidiagonals of the array: A007318 * A002260(transposed).
%C Antidiagonals tend to A001792 staring from the right: (1, 3, 8, 20, 48, 112, ...).
%F Antidiagonals of the array: A007318 * A002260(transform), where A002260 = (1; 1,2; 1,2,3; ...).
%e First few rows of the array:
%e 1, 1, 1, 1, 1, 1, ...;
%e 1, 3, 3, 3, 3, 3, ...;
%e 1, 5, 8, 8, 8, 8, ...;
%e 1, 7, 16, 20, 20, 20, ...;
%e 1, 9, 27, 43, 48, 48, ...;
%e 1, 11, 41, 81, 106, 112, ...;
%e ...
%e First few rows of the triangle:
%e 1;
%e 1, 1;
%e 1, 3, 1;
%e 1, 5, 3, 1;
%e 1, 7, 8, 3, 1;
%e 1, 9, 16, 8, 3, 1;
%e 1, 11, 27, 20, 8, 3, 1;
%e 1, 13, 41, 43, 20, 8, 3, 1;
%e ...
%p A002260 := proc(n,k)
%p if n <= k then
%p n+1;
%p else
%p 0 ;
%p end if;
%p end proc:
%p A007318 := proc(n,k)
%p if k <= n then
%p binomial(n,k) ;
%p else
%p 0
%p end if;
%p end proc:
%p A134836 := proc(n,k)
%p add( A007318(n,i)*A002260(i,k),i=0..k) ;
%p end proc:
%p seq(seq(A134836(d-k,k),k=0..d),d=0..12) ; # _R. J. Mathar_, Aug 17 2022
%Y Cf. A002260, A001792, A116445 (array transposed), A001629 (antidiagonal sums).
%K nonn,tabl,easy
%O 1,5
%A _Gary W. Adamson_, Nov 12 2007
%E One term corrected by _R. J. Mathar_, Aug 17 2022
|
