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 A127096 Triangle T(n,m) = A000012*A127094 read by rows. 5
 1, 3, 1, 6, 1, 1, 10, 1, 3, 1, 15, 1, 3, 1, 1, 21, 1, 3, 4, 3, 1, 28, 1, 3, 4, 3, 1, 1, 36, 1, 3, 4, 7, 1, 3, 1, 45, 1, 3, 4, 7, 1, 6, 1, 1, 55, 1, 3, 4, 7, 6, 6, 1, 3, 1, 66, 1, 3, 4, 7, 6, 6, 1, 3, 1, 1, 78, 1, 3, 4, 7, 6, 12, 1, 7, 4, 3, 1, 91, 1, 3, 4, 7, 6, 12, 1, 7, 4, 3, 1, 1, 105, 1, 3, 4, 7, 6, 12, 8, 7, 4, 3, 1, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Consider A000012 as a lower-left all-1's triangle, and build the matrix product by multiplication with A127094 from the right. LINKS Table of n, a(n) for n=1..105. FORMULA T(n,m) = Sum_{j=m..n} A000012(n,j)*A127094(j,m) = Sum_{j=m..n} A127094(j,m). EXAMPLE First few rows of the triangle are: 1; 3, 1, 6, 1, 1; 10, 1, 3, 1; 15, 1, 3, 1, 1; 21, 1, 3, 4, 3, 1; 28, 1, 3, 4, 3, 1, 1; ... MAPLE A127093 := proc(n, m) if n mod m = 0 then m; else 0 ; fi; end: A127094 := proc(n, m) A127093(n, n-m+1) ; end: A127096 := proc(n, m) add( A127094(j, m), j=m..n) ; end: for n from 1 to 15 do for m from 1 to n do printf("%d, ", A127096(n, m)) ; od: od: # R. J. Mathar, Aug 18 2009 MATHEMATICA T[n_, m_] := Sum[1 + Mod[j, m - j - 1] - Mod[1 + j, m - j - 1], {j, m, n}]; Table[T[n, m], {n, 1, 14}, {m, 1, n}] // Flatten (* Jean-François Alcover, Sep 15 2023 *) CROSSREFS Cf. A127093, A127094, A123229, A024916 (row sums), A000203, A126988. Sequence in context: A124846 A177375 A099512 * A130541 A128489 A034839 Adjacent sequences: A127093 A127094 A127095 * A127097 A127098 A127099 KEYWORD nonn,easy,tabl AUTHOR Gary W. Adamson, Jan 05 2007 EXTENSIONS Edited and extended by R. J. Mathar, Aug 18 2009 STATUS approved

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Last modified August 8 14:00 EDT 2024. Contains 375021 sequences. (Running on oeis4.)