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A160770
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Triangle in which row n is generated from (1,3,6,10,...n)dot(n,n-1,...1) with subtractive carryovers.
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2
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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
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OFFSET
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0,2
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COMMENTS
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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,...).
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LINKS
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FORMULA
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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.
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EXAMPLE
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First few rows of the triangle =
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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).
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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