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 A284115 Hosoya triangle of Lucas type. 1
 1, 3, 3, 4, 9, 4, 7, 12, 12, 7, 11, 21, 16, 21, 11, 18, 33, 28, 28, 33, 18, 29, 54, 44, 49, 44, 54, 29, 47, 87, 72, 77, 77, 72, 87, 47, 76, 141, 116, 126, 121, 126, 116, 141, 76, 123, 228, 188, 203, 198, 198, 203, 188, 228, 123, 199, 369, 304, 329, 319, 324, 319, 329, 304, 369, 199 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Indranil Ghosh, Rows 1..100, flattened Matthew Blair, Rigoberto Flórez, Antara Mukherjee, Matrices in the Hosoya triangle, arXiv:1808.05278 [math.CO], 2018. H. Hosoya, Fibonacci Triangle, The Fibonacci Quarterly, 14;2, 1976, 173-178. 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. Wikipedia, Hosoya triangle FORMULA T(n,k) = L(k)*L(n - k + 1), L(.) is a Lucas number. EXAMPLE Triangle begins: 1; 3, 3; 4, 9, 4; 7, 12, 12, 7; 11, 21, 16, 21, 11; 18, 33, 28, 28, 33, 18; 29, 54, 44, 49, 44, 54, 29; ... MATHEMATICA Table[LucasL[k] LucasL[n - k + 1] , {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Mar 31 2017 *) PROG (PARI) L(n) = fibonacci(n + 2) - fibonacci(n - 2); for(n=1, 10, for(k=1, n, print1(L(k) * L(n - k + 1), ", "); ); print(); ) \\ Indranil Ghosh, Mar 31 2017 (Python) from sympy import lucas for n in range(1, 11): ....print [lucas(k) * lucas(n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, Mar 31 2017 CROSSREFS Cf. A000032. Sequence in context: A197431 A197672 A348884 * A183501 A086239 A016605 Adjacent sequences: A284112 A284113 A284114 * A284116 A284117 A284118 KEYWORD nonn,tabl AUTHOR Rigoberto Florez, Mar 20 2017 STATUS approved

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Last modified February 1 07:16 EST 2023. Contains 359981 sequences. (Running on oeis4.)