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 A127779 Triangle read by rows: A004736 * A127773. 1
 1, 2, 3, 3, 6, 6, 4, 9, 12, 10, 5, 12, 18, 20, 15, 6, 15, 24, 30, 30, 21, 7, 18, 30, 40, 45, 42, 28, 8, 21, 36, 50, 60, 63, 56, 36, 9, 24, 42, 60, 75, 84, 84, 72, 45 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums = bin(n,4), (A000332): (1, 5, 15, 35, ...). From Clark Kimberling, Sep 16 2008: (Start) As a rectangular array: R = A000027*A000217; R(m,n) = n*binomial(m+1,2). R is the accumulation array (cf. A144112) of A002260 (rectangular, with n-th row (n,n,n,n,...). (End) As a rectangular array read by ascending antidiagonals, T(n,k) is the total number of triangles obtained when a triangle is cut into n parts with segments going down from the apex to its base and into k parts with segments parallel to its base. See Quora link. - Michel Marcus, Apr 07 2023 LINKS Table of n, a(n) for n=1..45. Quora, How many triangles are in this picture?. FORMULA A004736 * A127773 as infinite lower triangular matrices. EXAMPLE First few rows of the triangle: 1; 2, 3; 3, 6, 6; 4, 9, 12, 10; 5, 12, 18, 20, 15; 6, 15, 24, 30, 30, 21; 7, 18, 30, 40, 45, 42, 28; ... First few rows of the rectangular array: 1 3 6 10 15 ... 2 6 12 20 30 ... 3 9 18 30 45 ... 4 12 24 40 60 ... 5 15 30 50 75 ... ... CROSSREFS Cf. A004736, A127773, A000217, A000332. Cf. A002260. - Clark Kimberling, Sep 16 2008 Sequence in context: A075258 A321745 A212629 * A207634 A222862 A101437 Adjacent sequences: A127776 A127777 A127778 * A127780 A127781 A127782 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jan 28 2007 STATUS approved

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Last modified April 16 01:01 EDT 2024. Contains 371696 sequences. (Running on oeis4.)