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 A160770 Triangle in which row n is generated from (1,3,6,10,...n)dot(n,n-1,...1) with subtractive carryovers. 2
 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, 18, 10, 36, 48, 78, 72, 78, 48, 36, 0, 45, 63, 105, 105, 120, 90, 78, 30, 15 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums = A005995: (1, 3, 12, 28, 66, 126, 236,...); also generated from: (1/2)*((1, 6, 21, 56, 126,...)+(1, 0, 3, 0, 6, 0, 10,...)); where (1, 6, 21,...) = bin(n,5). A177878 = the analogous sequence using vector (1,2,3,...). LINKS FORMULA 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. EXAMPLE First few rows of the triangle = . 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, 18, 10; 36, 48, 78, 72, 78, 48, 36, 0 45, 63, 105, 105, 120, 90, 78, 30, 15; ... 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). CROSSREFS Sequence in context: A085753 A120008 A162197 * A212225 A278085 A051021 Adjacent sequences:  A160767 A160768 A160769 * A160771 A160772 A160773 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Dec 15 2010 STATUS approved

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Last modified February 21 03:06 EST 2019. Contains 320364 sequences. (Running on oeis4.)