The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A284129 Hosoya triangle Jacobsthal Lucas type. 1
 1, 5, 5, 7, 25, 7, 17, 35, 35, 17, 31, 85, 49, 85, 31, 65, 155, 119, 119, 155, 65, 127, 325, 217, 289, 217, 325, 127, 257, 635, 455, 527, 527, 455, 635, 257, 511, 1285, 889, 1105, 961, 1105, 889, 1285, 511, 1025, 2555, 1799, 2159, 2015, 2015, 2159, 1799, 2555, 1025, 2047, 5125 (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, pages 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), pages 163-174. Wikipedia, Hosoya's triangle. FORMULA T(n,k) = A014551(k)*A014551(n - k + 1), where n > 0 and 0 < k <= n. EXAMPLE Triangle begins: 1, 5, 5, 7, 25, 7, 17, 35, 35, 17, 31, 85, 49, 85, 31, 65, 155, 119, 119, 155, 65, 127, 325, 217, 289, 217, 325, 127, 257, 635, 455, 527, 527, 455, 635, 257, 511, 1285, 889, 1105, 961, 1105, 889, 1285, 511, ... MATHEMATICA a[n_]:= 2^n + (-1)^n; Table[a[k] a[n - k + 1], {n, 10}, {k, n}] // Flatten (* Indranil Ghosh, Mar 30 2017 *) PROG (PARI) a(n) = 2^n + (-1)^n; for(n=1, 10, for(k=1, n, print1(a(k)*a(n - k + 1), ", "); ); print(); ); \\ Indranil Ghosh, Mar 30 2017 (Python) def a(n): return 2**n + (-1)**n for n in range(1, 11): ....print [a(k) * a(n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, Mar 30 2017 CROSSREFS Cf. A014551. Sequence in context: A109257 A088048 A006146 * A077956 A077977 A019204 Adjacent sequences: A284126 A284127 A284128 * A284130 A284131 A284132 KEYWORD nonn,tabl AUTHOR Rigoberto Florez, Mar 20 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 1 06:22 EST 2023. Contains 359981 sequences. (Running on oeis4.)