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A284128
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Hosoya triangle of Fermat Lucas type, read by rows.
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0
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9, 15, 15, 27, 25, 27, 51, 45, 45, 51, 99, 85, 81, 85, 99, 195, 165, 153, 153, 165, 195, 387, 325, 297, 289, 297, 325, 387, 771, 645, 585, 561, 561, 585, 645, 771, 1539, 1285, 1161, 1105, 1089, 1105, 1161, 1285, 1539, 3075, 2565, 2313, 2193, 2145, 2145, 2193, 2313, 2565, 3075
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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9,1
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LINKS
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Table of n, a(n) for n=9..63.
R. Florez, R. Higuita and L. Junes, GCD property of the generalized star of David in the generalized Hosoya triangle, J. Integer Seq., 17 (2014), Article 14.3.6, 17 pp.
R. Florez and L. Junes, GCD properties in Hosoya's triangle, Fibonacci Quart. 50 (2012), 163-174.
H. Hosoya, Fibonacci Triangle, The Fibonacci Quarterly, 14;2, 1976, 173-178.
Wikipedia, Hosoya triangle
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FORMULA
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T(n,k) = (2^k + 1)*(2^(n - k + 1) + 1) n > 0, 0 < k <= n.
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EXAMPLE
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Triangle begins:
9;
15, 15;
27, 25, 27;
51, 45, 45, 51;
99, 85, 81, 85, 99;
195, 165, 153, 153, 165, 195;
...
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MATHEMATICA
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Table[(2^k + 1) (2^(n - k + 1) + 1), {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Apr 02 2017 *)
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PROG
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(PARI) T(n, k) = (2^k + 1)*(2^(n - k + 1) + 1);
tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Apr 02 2017
(Python)
for n in range(1, 11):
....print [(2**k + 1) * (2**(n - k + 1) + 1) for k in range(1, n + 1)] # Indranil Ghosh, Apr 02 2017
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CROSSREFS
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Sequence in context: A346609 A232395 A184048 * A058957 A257409 A105882
Adjacent sequences: A284125 A284126 A284127 * A284129 A284130 A284131
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KEYWORD
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nonn,tabl
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AUTHOR
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Rigoberto Florez, Mar 20 2017
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STATUS
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approved
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