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A174828
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An averaging sum sequence based on:a(n,m)=Floor[(a(n - 1, m - 1) + a(n - 1, m))/2] with limit q
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0
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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
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OFFSET
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0,3
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COMMENTS
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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}
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LINKS
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Table of n, a(n) for n=0..79.
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FORMULA
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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}]
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EXAMPLE
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{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}
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MATHEMATICA
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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[%]
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CROSSREFS
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Sequence in context: A177226 A059026 A104471 * A085643 A174829 A132110
Adjacent sequences: A174825 A174826 A174827 * A174829 A174830 A174831
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Mar 30 2010
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STATUS
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approved
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