|
%I #11 Mar 12 2022 13:07:57
%S 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 18,10,36,48,78,72,78,48,36,0,45,63,105,105,120,90,78,30,15
%N Triangle in which row n is generated from (1,3,6,10,...n)dot(n,n-1,...1) with subtractive carryovers.
%C Row sums = A005995: (1, 3, 12, 28, 66, 126, 236,...); also generated from:
%C (1/2)*((1, 6, 21, 56, 126,...)+(1, 0, 3, 0, 6, 0, 10,...)); where (1, 6, 21,...) = bin(n,5).
%C A177878 = the analogous sequence using vector (1,2,3,...).
%F 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 First few rows of the triangle =
%e .
%e 1;
%e 3, 0;
%e 6, 3, 3;
%e 10, 8, 10, 0;
%e 15, 15, 21, 9, 6;
%e 21, 24, 36, 24, 21, 0;
%e 28, 35, 55, 45, 45, 18, 10;
%e 36, 48, 78, 72, 78, 48, 36, 0
%e 45, 63, 105, 105, 120, 90, 78, 30, 15;
%e ...
%e 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 A005995, A177878
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Dec 15 2010
|
