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A158753
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Lucas even count down recursion:e(n,k)=(e(n - 1, k)*e(n, k - 1) + 1)/e(n - 1, k - 1)
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1
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1, 4, 1, 11, 4, 1, 29, 11, 4, 1, 76, 29, 11, 4, 1, 199, 76, 29, 11, 4, 1, 521, 199, 76, 29, 11, 4, 1, 1364, 521, 199, 76, 29, 11, 4, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| Really slow backward recursion in Mathematica.
Row sums are:A004146;
{1, 5, 16, 45, 121,320, 841, 2205,...}.
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REFERENCES
| H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162
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FORMULA
| Every other result is a beta integer ( odd Phi factors, even Integers): e(n,k)=(e(n - 1, k)*e(n, k - 1) + 1)/e(n - 1, k - 1)
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EXAMPLE
| {1},
{4, 1},
{11, 4, 1},
{29, 11, 4, 1},
{76, 29, 11, 4, 1},
{199,76, 29, 11, 4, 1},
{521,199,76, 29, 11, 4, 1},
{1364,521,199,76, 29, 11, 4, 1}
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MATHEMATICA
| Clear[e, n, k];
e[n_, 0] := GoldenRatio^n - GoldenRatio^(-n);
e[n_, k_] := 0 /; k >= n;
e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
Table[Table[ Rationalize[N[e[n, k]]], {k, Mod[n, 2] + 1, n - 1, 2}], {n, 2, 16, 2}];
Flatten[%]
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CROSSREFS
| A002878, A004146
Sequence in context: A178519 A094503 A113897 * A183884 A135552 A181690
Adjacent sequences: A158750 A158751 A158752 * A158754 A158755 A158756
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 25 2009
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