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A284126 Hosoya triangle of Pell-Lucas type. 1
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)
OFFSET

1,1

LINKS

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

FORMULA

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.

EXAMPLE

Triangle begins:

4;

12, 12;

28, 36, 28;

68, 84, 84, 68;

164, 204, 196, 204, 164;

...

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A195199 A294628 A323188 * A272841 A272942 A272923

Adjacent sequences: A284123 A284124 A284125 * A284127 A284128 A284129

KEYWORD

nonn,tabl

AUTHOR

Rigoberto Florez, Mar 20 2017

STATUS

approved

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Last modified February 1 07:10 EST 2023. Contains 359981 sequences. (Running on oeis4.)