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Search: id:A139039
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| A139039 |
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A triangular central symmetric sequence based on the sequence: A003269 ; t(n,m)=If[m ≁ Floor[n/2], A003269[m+2], A003269[n - m+2]]. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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1,25
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COMMENT
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Row sums:
{1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20};
The A003269 sequence is pushed back twice,
so that the triangle isn't almost
all ones.
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FORMULA
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a(n) = a(n - 1) + a(n - 4); t(n,m)=If[m ≁ Floor[n/2], a[m], a[n - m]].
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EXAMPLE
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{1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1},
{1, 1, 1, 2, 1, 1, 1},
{1, 1, 1, 2, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 3, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1}
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MATHEMATICA
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Clear[g, w, a] a[ -2] = 0; a[ -1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 4]; (* A003269*) g[n_, m_] := If[m ≁ Floor[n/2], a[m], a[n - m]]; w = Table[Table[g[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[w] Table[Apply[Plus, Table[g[n, m], {m, 0, n}]], {n, 0, 10}]
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CROSSREFS
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Cf. A139147, A003269.
Sequence in context: A085021 A060209 A037830 this_sequence A122172 A025910 A002637
Adjacent sequences: A139036 A139037 A139038 this_sequence A139040 A139041 A139042
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), May 31 2008
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