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 A284131 Hosoya triangle of Morgan Voyce type, read by rows. 0
 9, 21, 21, 54, 49, 54, 141, 126, 126, 141, 369, 329, 324, 329, 369, 966, 861, 846, 846, 861, 966, 2529, 2254, 2214, 2209, 2214, 2254, 2529, 6621, 5901, 5796, 5781, 5781, 5796, 5901, 6621, 17334, 15449, 15174, 15134, 15129, 15134, 15174, 15449, 17334, 45381, 40446, 45381 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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. Eric Weisstein's World of Mathematics, Morgan-Voyce polynomials Wikipedia, Hosoya Triangle FORMULA T(n,k) = L(2k)L(2(n - k + 1)), L(.) is a Lucas number; 0 < n, 0 < k <= n. EXAMPLE Triangle begins:     9;    21,  21;    54,  49,  54;   141, 126, 126, 141;   369, 329, 324, 329, 369;   ... MATHEMATICA Table[LucasL[2k] LucasL[2(n - k + 1)], {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Mar 30 2017 *) PROG (PARI) L(n) = fibonacci(n + 2) - fibonacci(n - 2); for(n=1, 10, for(k=1, n, print1(L(2*k)*L(2*(n - k + 1)), ", "); ); print(); ); \\ Indranil Ghosh, Mar 30 2017 (Python) from sympy import lucas for n in range(1, 11): ....print [lucas(2*k) * lucas(2*(n - k + 1)) for k in range(1, n + 1)] # Indranil Ghosh, Mar 30 2017 CROSSREFS Cf. A000032. Sequence in context: A250783 A259250 A251219 * A111171 A317789 A333039 Adjacent sequences:  A284128 A284129 A284130 * A284132 A284133 A284134 KEYWORD nonn,tabl AUTHOR Rigoberto Florez, Mar 20 2017 STATUS approved

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Last modified June 14 12:04 EDT 2021. Contains 345025 sequences. (Running on oeis4.)