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A284126
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Hosoya triangle of Pell-Lucas type.
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1
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4, 12, 12, 28, 36, 28, 68, 84, 84, 68, 164, 204, 196, 204, 164, 396, 492, 476, 476, 492, 396, 956, 1188, 1148, 1156, 1148, 1188, 956, 2308, 2868, 2772, 2788, 2788, 2772, 2868, 2308, 5572, 6924, 6692, 6732, 6724, 6732, 6692, 6924, 5572, 13452, 16716, 16156, 16252, 16236, 16236, 16252, 16156, 16716, 13452
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..11325 rows 1 <= n <= 150.
Matthew Blair, Rigoberto Flórez, Antara Mukherjee, Matrices in the Hosoya triangle, arXiv:1808.05278 [math.CO], 2018.
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.
Wikipedia, Hosoya triangle
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FORMULA
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T(n, k)= a(k)*a(n - k + 1), a (n) = 2 a (n - 1) + a (n - 2), a (0) = a (1) = 2; 0 < n, 0 < k <= n.
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EXAMPLE
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Triangle begins:
4;
12, 12;
28, 36, 28;
68, 84, 84, 68;
164, 204, 196, 204, 164;
...
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MATHEMATICA
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a[n_]:= a[n]=If[n<2, 2, 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 *)
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PROG
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(PARI) a(n) = if(n<2, 2, 2*a(n - 1) + a(n - 2));
for(n=1, 20, for(k=1, n, print1(a(k)*a(n - k + 1), ", "); ); print(); ) \\ Indranil Ghosh, Apr 08 2017
(Python)
def a(n): return 2 if n<2 else 2*a(n - 1) + a(n - 2)
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
(C)
#include <stdio.h>
int a(int n){
if(n<2){ return 2; }
return 2*a(n - 1) + a(n - 2);
}
int main()
{
int n, k;
for (n=1; n<=20; n++){
for(k=1; k<=n; k++){
printf("%d, ", a(k)*a(n - k + 1));
}
printf("\n");
}
return 0;
} // Indranil Ghosh, Apr 08 2017
(Go)
package main
import "fmt"
func a(n int)int{
if n<2{ return 2 }
return 2*a(n - 1) + a(n - 2)}
func main() {
for n:=1; n<=20; n++{
for k:=1; k<=n; k++{
fmt.Printf("%d, ", a(k)*a(n - k + 1))}
fmt.Println()}
} // Indranil Ghosh, Apr 08 2017
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CROSSREFS
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Sequence in context: A195199 A294628 A323188 * A272841 A272942 A272923
Adjacent sequences: A284123 A284124 A284125 * A284127 A284128 A284129
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KEYWORD
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nonn,tabl
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AUTHOR
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Rigoberto Florez, Mar 20 2017
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STATUS
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approved
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