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 A174828 An averaging sum sequence based on:a(n,m)=Floor[(a(n - 1, m - 1) + a(n - 1, m))/2] with limit q 0
 1, 1, 2, 1, 3, 4, 1, 4, 5, 7, 1, 5, 6, 8, 10, 1, 6, 7, 9, 11, 14, 1, 7, 8, 10, 12, 15, 18, 1, 8, 9, 11, 13, 16, 19, 23, 1, 9, 10, 12, 14, 17, 20, 24, 28, 1, 10, 11, 13, 15, 18, 21, 25, 29, 34, 1, 11, 12, 14, 16, 19, 22, 26, 30, 35, 40, 1, 12, 13, 15, 17, 20, 23, 27, 31, 36, 41, 47, 1, 13 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums are: {1, 3, 8, 17, 30, 48, 71, 100, 135, 177, 226, 283, 348,...}. Example a(n,m) for q=10: {1}, {1, 10}, {1, 1, 10}, {1, 1, 2, 10}, {1, 1, 1, 3, 10}, {1, 1, 1, 2, 4, 10}, {1, 1, 1, 1, 3, 5, 10}, {1, 1, 1, 1, 2, 4, 6, 10}, {1, 1, 1, 1, 1, 3, 5, 7, 10}, {1, 1, 1, 1, 1, 2, 4, 6, 8, 10}, {1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 10} LINKS FORMULA a(n,m)=Floor[(a(n - 1, m - 1) + a(n - 1, m))/2] with limit q: t(n,q)=Sum(a(n,m),{m,0,q}] EXAMPLE {1}, {1, 2}, {1, 3, 4}, {1, 4, 5, 7}, {1, 5, 6, 8, 10}, {1, 6, 7, 9, 11, 14}, {1, 7, 8, 10, 12, 15, 18}, {1, 8, 9, 11, 13, 16, 19, 23}, {1, 9, 10, 12, 14, 17, 20, 24, 28}, {1, 10, 11, 13, 15, 18, 21, 25, 29, 34}, {1, 11, 12, 14, 16, 19, 22, 26, 30, 35, 40}, {1, 12, 13, 15, 17, 20, 23, 27, 31, 36, 41, 47}, {1, 13, 14, 16, 18, 21, 24, 28, 32, 37, 42, 48, 54} MATHEMATICA Clear[a, n, m, N0]; N0 = q; a[0, 0] := 1; a[1, 0] := 1; a[1, 1] = N0; a[n_, 0] := 1; a[n_, n_] := N0; a[n_, m_] := a[n, m] = Floor[(a[n - 1, m - 1] + a[n - 1, m])/2] Table[Table[Sum[a[n, m], {m, 0, n}], {n, 0, q}], {q, 0, 12}]; Flatten[%] CROSSREFS Sequence in context: A177226 A059026 A104471 * A085643 A174829 A132110 Adjacent sequences:  A174825 A174826 A174827 * A174829 A174830 A174831 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Mar 30 2010 STATUS approved

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