cp's OEIS Frontend

A134394 Triangle T(n,k) = Sum_{j=k..n} A077028(j,k), read by rows.

%I A134394 #15 Jun 01 2022 08:16:07
%S A134394 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 A134394 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 A134394 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 A134394 Triangle T(n,k) = Sum_{j=k..n} A077028(j,k), read by rows.
%C A134394 Row sums = A055795: (1, 3, 7, 15, 30, 56, 98, ...).
%C A134394 Antidiagonal reading of A139600 without its left column. - _R. J. Mathar_, Apr 17 2011
%F A134394 A000012 * A077028 as infinite lower triangular matrices.
%F A134394 T(n,k) = (k-n-1)*(k*(k-n)-2)/2. - _R. J. Mathar_, Apr 17 2011
%e A134394 First few rows of the triangle:
%e A134394   1;
%e A134394   2,  1;
%e A134394   3,  3,  1;
%e A134394   4,  6,  4,  1;
%e A134394   5, 10,  9,  5,  1;
%e A134394   6, 15, 16, 12,  6,  1;
%e A134394   7, 21, 25, 22, 15,  7,  1;
%p A134394 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 A134394 := proc(n,k) add ( A077028(j,k),j=k..n) ; end proc:
%p A134394 seq(seq(A134394(n,k),k=0..n),n=0..15) ; # _R. J. Mathar_, Apr 17 2011
%Y A134394 Cf. A077028, A055795, A139600.
%K A134394 nonn,tabl
%O A134394 1,2
%A A134394 _Gary W. Adamson_, Oct 23 2007