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A284130 Hosoya triangle of Jacobsthal type, read by rows. 1

%I

%S 1,1,1,3,1,3,5,3,3,5,11,5,9,5,11,21,11,15,15,11,21,43,21,33,25,33,21,

%T 43,85,43,63,55,55,63,43,85,171,85,129,105,121,105,129,85,171,341,171,

%U 255,215,231,231,215,255,171,341,683,341,513,425,473,441,473,425,513,341,683

%N Hosoya triangle of Jacobsthal type, read by rows.

%H Michael De Vlieger, <a href="/A284130/b284130.txt">Table of n, a(n) for n = 1..11026</a>, rows 1 <= n <= 150.

%H Matthew Blair, Rigoberto Flórez, Antara Mukherjee, <a href="https://arxiv.org/abs/1808.05278">Matrices in the Hosoya triangle</a>, arXiv:1808.05278 [math.CO], 2018.

%H R. Florez, R. Higuita and L. Junes, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Florez/florez3.html">GCD property of the generalized star of David in the generalized Hosoya triangle</a>, J. Integer Seq., 17 (2014), Article 14.3.6, 17 pp.

%H R. Florez and L. Junes, <a href="http://leandrojunes.com/wp-content/uploads/2014/07/FlorezJunes.pdf">GCD properties in Hosoya's triangle</a>, Fibonacci Quart. 50 (2012), 163-174.

%H H. Hosoya, <a href="http://www.fq.math.ca/Scanned/14-2/hosoya.pdf">Fibonacci Triangle</a>, The Fibonacci Quarterly, 14;2, 1976, 173-178.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hosoya%27s_triangle">Hosoya triangle</a>

%F T(n,k) = A001045(k)*A001045(n - k + 1), 0 < n, 0 < k <= n.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 3, 1, 3;

%e 5, 3, 3, 5;

%e 11, 5, 9, 5, 11;

%e 21, 11, 15, 15, 11, 21;

%e ...

%t With[{s = Array[(2^# - (-1)^#)/3 &, 150, 0]}, Table[s[[k]] s[[n - k + 1]], {n, Length@ s}, {k, 2, n - 1}]] // Flatten (* _Michael De Vlieger_, Nov 14 2018, after Joseph Biberstine at A001045 *)

%o (PARI) a(n) = if(n<2, n, a(n - 1) + 2*a(n - 2));

%o for(n=0, 15, for(k=1, n, print1(a(k) * a(n - k + 1),", ");); print();); \\ _Indranil Ghosh_, Mar 29 2017

%Y Cf. A001045.

%K nonn,tabl

%O 1,4

%A _Rigoberto Florez_, Mar 20 2017

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Last modified June 13 00:57 EDT 2021. Contains 344980 sequences. (Running on oeis4.)