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A139038
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Centrally symmetric triangle read by rows: t(n,m)=If(m <= Floor(n/2), A000931(m+1), A000931(n - m+1)).
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4
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 3, 4, 3, 2, 2, 1
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OFFSET
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1,13
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COMMENTS
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Row sums: {1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 22, ...}.
The Padovan sequence is pushed back to a[-1]=1, so that the triangle is not almost all ones.
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LINKS
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Table of n, a(n) for n=1..65.
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FORMULA
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a(n) = a(n-2) + a(n-3); 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, 2, 1, 1},
{1, 1, 2, 2, 1, 1},
{1, 1, 2, 2, 2, 1, 1},
{1, 1, 2, 2, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 3, 2, 2, 1, 1},
{1, 1, 2, 2, 3, 4, 3, 2, 2, 1, 1}
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MATHEMATICA
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Clear[a] a[ -1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; (* Padovan : A000931 *) Table[If[m <= Floor[n/2], a[m], a[n - m]], {n, 0, 10}, {m, 0, n}]
(* Alternative Mathematica function*) t[n_, m_] = Min[1 + Floor[m/2], 1 + Floor[(n - m)/2]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
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CROSSREFS
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Cf. A139147.
Sequence in context: A155052 A096284 A163100 * A139040 A139147 A055801
Adjacent sequences: A139035 A139036 A139037 * A139039 A139040 A139041
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson, May 31 2008
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EXTENSIONS
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Edited by N. J. A. Sloane, Feb 28 2009
Corrected non-ascii characters in %t line Wouter Meeussen, Feb 10 2013
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STATUS
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approved
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