A134394 - OEIS

%I #15 Jun 01 2022 08:16:07

%S 1,2,1,3,3,1,4,6,4,1,5,10,9,5,1,6,15,16,12,6,1,7,21,25,22,15,7,1,8,28,

%T 36,35,28,18,8,1,9,36,49,51,45,34,21,9,1,10,45,64,70,66,55,40,24,10,1,

%U 11,55,81,92,91,81,65,46,27,11,1,12,66,100,117,120,112,96,75,52,30,12,1,13,78,121,145,153

%N Triangle T(n,k) = Sum_{j=k..n} A077028(j,k), read by rows.

%C Row sums = A055795: (1, 3, 7, 15, 30, 56, 98, ...).

%C Antidiagonal reading of A139600 without its left column. - _R. J. Mathar_, Apr 17 2011

%F A000012 * A077028 as infinite lower triangular matrices.

%F T(n,k) = (k-n-1)*(k*(k-n)-2)/2. - _R. J. Mathar_, Apr 17 2011

%e First few rows of the triangle:

%e   1;

%e   2,  1;

%e   3,  3,  1;

%e   4,  6,  4,  1;

%e   5, 10,  9,  5,  1;

%e   6, 15, 16, 12,  6,  1;

%e   7, 21, 25, 22, 15,  7,  1;

%p A077028 := proc(n,k) if n < 0 or k<0 or k > n then 0; else k*(n-k)+1 ; end if; end proc:

%p A134394 := proc(n,k) add ( A077028(j,k),j=k..n) ; end proc:

%p seq(seq(A134394(n,k),k=0..n),n=0..15) ; # _R. J. Mathar_, Apr 17 2011

%Y Cf. A077028, A055795, A139600.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Oct 23 2007