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 A128227 Right border (1,1,1,...) added to A002260. 7
 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 4, 1, 1, 2, 3, 4, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums = A000124: (1, 2, 4, 7, 11, 16, ...). n* each term of the triangle gives A128228, having row sums A006000: (1, 4, 12, 28, 55, ...). Eigensequence of the triangle = A005425: (1, 2, 5, 14, 43, ...). - Gary W. Adamson, Aug 27 2010 From Franck Maminirina Ramaharo, Aug 25 2018: (Start) T(n,k) is the number of binary words of length n having k letters 1 such that no 1's lie between any pair of 0's. Let n lines with equations y = (i - 1)*x - (i - 1)^2, i = 1..n, be drawn in the Cartesian plane. For each line, call the half plane containing the point (-1,1) the upper half plane and the other half the lower half-plane. Then T(n,k) is the number of regions that are the intersections of k upper half-planes and n-k lower half-planes. Here, T(0,0) = 1 corresponds to the plane itself. A region obtained from this arrangement of lines can be associated with a length n binary word such that the i-th letter indicates whether the region is located at the i-th upper half-plane (letter 1) or at the lower half-plane (letter 0). (End) LINKS A. Bogolmony, Number of Regions N Lines Divide Plane. Eric Weisstein's World of Mathematics, Plane Division by Lines. J. E. Wetzel, On the division of the plane by lines, The American Mathematical Monthly Vol. 85 (1978), 647-656. FORMULA "1" added to each row of "start counting again": (1; 1,2; 1,2,3,...) such that a(1) = 1, giving: (1; 1,1; 1,2,1;...). T(n,k) = k if 1<=k

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Last modified August 4 02:10 EDT 2020. Contains 336201 sequences. (Running on oeis4.)