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%I #36 Dec 07 2019 12:18:28
%S 1,2,2,5,4,5,12,10,10,12,29,24,25,24,29,70,58,60,60,58,70,169,140,145,
%T 144,145,140,169,408,338,350,348,348,350,338,408,985,816,845,840,841,
%U 840,845,816,985,2378,1970,2040,2028,2030,2030,2028,2040,1970,2378,5741,4756,4925,4896,4901,4900,4901,4896,4925,4756,5741
%N Hosoya triangle of Pell type, read by rows.
%H Michael De Vlieger, <a href="/A284127/b284127.txt">Table of n, a(n) for n = 1..11325</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) = a(k)*a(n - k + 1), a(n) = 2*a (n - 1) + a (n - 2), with a(0) = 0, a(1) = 1; for 0 < n, 0 < k <= n.
%e Triangle begins:
%e 1;
%e 2, 2;
%e 5, 4, 5;
%e 12, 10, 10, 12;
%e 29, 24, 25, 24, 29;
%e 70, 58, 60, 60, 58, 70;
%e ...
%t a[n_]:=a[n]=If[n<2, n, 2a[n - 1] + a[n - 2]]; Table[a[k] a[n - k + 1], {n, 20}, {k, n}] // Flatten (* _Indranil Ghosh_, Apr 08 2017, edited by _Michael De Vlieger_, Nov 14 2018 *)
%o (PARI) a(n) = if(n<2, n, 2*a(n - 1) + a(n - 2));
%o for(n=1, 20, for(k=1, n, print1(a(k)*a(n - k + 1),", ");); print();) \\ _Indranil Ghosh_, Apr 08 2017
%o (Python)
%o def a(n): return n if n<2 else 2*a(n - 1) + a(n - 2)
%o for n in range(1, 21): print [a(k)*a(n - k + 1) for k in range(1, n + 1)] # _Indranil Ghosh_, Apr 08 2017
%o (C)
%o #include <stdio.h>
%o int a(int n){
%o if(n<2){ return n;}
%o return 2*a(n - 1) + a(n - 2);
%o }
%o int main()
%o {
%o int n, k;
%o for (n=1; n<=20; n++){
%o for(k=1; k<=n; k++){
%o printf("%d, ", a(k)*a(n - k + 1));
%o }
%o printf("\n");
%o }
%o return 0;
%o } // _Indranil Ghosh_, Apr 08 2017
%o (Go)
%o package main
%o import "fmt"
%o func a(n int)int{
%o if n<2{ return n }
%o return 2*a(n - 1) + a(n - 2)}
%o func main() {
%o for n:=1; n<=20; n++{
%o for k:=1; k<=n; k++{
%o fmt.Printf("%d, ",a(k)*a(n - k + 1))}
%o fmt.Println()
%o }
%o } // _Indranil Ghosh_, Apr 08 2017
%K nonn,tabl
%O 1,2
%A _Rigoberto Florez_, Mar 20 2017
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