cp's OEIS Frontend

A160770 Triangle in which row n is generated from (1,3,6,10,...n) dot (n,n-1,...1) with subtractive carryovers.

%I A160770 #14 Feb 04 2025 23:37:57
%S A160770 1,3,0,6,3,3,10,8,10,0,15,15,21,9,6,21,24,36,24,21,0,28,35,55,45,45,
%T A160770 18,10,36,48,78,72,78,48,36,0,45,63,105,105,120,90,78,30,15
%N A160770 Triangle in which row n is generated from (1,3,6,10,...n) dot (n,n-1,...1) with subtractive carryovers.
%C A160770 Row sums = A005995: (1, 3, 12, 28, 66, 126, 236,...); also generated from:
%C A160770 (1/2)*((1, 6, 21, 56, 126,...)+(1, 0, 3, 0, 6, 0, 10,...)); where (1, 6, 21,...) = bin(n,5).
%C A160770 A177878 = the analogous sequence using vector (1,2,3,...).
%F A160770 The subtractive carryover dot product of two vectors (a(1),a(2),...a(n)) dot (b(1),b(2),..b(n)) = (c(1),..,c(n)) is defined by c(1)=a(1)*b(1) and c(i) = a(i)*b(i)-c(i-1), i>1; where the vector = the triangular series.
%e A160770 First few rows of the triangle:
%e A160770   1;
%e A160770   3, 0;
%e A160770   6, 3, 3;
%e A160770   10, 8, 10, 0;
%e A160770   15, 15, 21, 9, 6;
%e A160770   21, 24, 36, 24, 21, 0;
%e A160770   28, 35, 55, 45, 45, 18, 10;
%e A160770   36, 48, 78, 72, 78, 48, 36, 0
%e A160770   45, 63, 105, 105, 120, 90, 78, 30, 15;
%e A160770   ...
%e A160770 Example: row 2 = (6, 3, 3) = (1, 3, 6) dot (6, 3, 1) with subtractive carryovers = ((1*6=6), (3*3-6=3), (6*1-3=3)) = (6, 3, 3).
%Y A160770 A005995, A177878
%K A160770 nonn,tabl
%O A160770 0,2
%A A160770 _Gary W. Adamson_, Dec 15 2010