

A094565


Triangle read by rows: binary products of Fibonacci numbers.


4



1, 2, 3, 5, 6, 8, 13, 15, 16, 21, 34, 39, 40, 42, 55, 89, 102, 104, 105, 110, 144, 233, 267, 272, 273, 275, 288, 377, 610, 699, 712, 714, 715, 720, 754, 987, 1597, 1830, 1864, 1869, 1870, 1872, 1885, 1974, 2584, 4181, 4791, 4880, 4893, 4895, 4896, 4901, 4935, 5168, 6765
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OFFSET

1,2


COMMENTS

Row n consists of n numbers, first F(2n1) and last F(2n).
Central numbers: (1,6,40,273,...) = A081016.
Alternating row sums: 1,1,7,7,48,48,329,329; the sequence b=(1,7,48,329,...) is A004187, given by b(n)=F(4n+2)b(n1) for n>=2, with b(1)=1.
In each row, the difference between neighboring terms is a Fibonacci number.


LINKS



FORMULA

Row n: F(2)F(2n1), F(4)F(2n3), ..., F(2n)F(1).


EXAMPLE

Triangle begins:
1;
2, 3;
5, 6 8;
13, 15, 16, 21;
34, 39, 40, 42, 55;
89, 102, 104, 105, 110, 144; ...


MATHEMATICA

Table[Fibonacci[2*k]*Fibonacci[2*n2*k+1], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Jul 15 2019 *)


PROG

(PARI) row(n) = vector(n, k, fibonacci(2*k)*fibonacci(2*n2*k+1));
tabl(nn) = for(n=1, nn, print(row(n))); \\ Michel Marcus, May 03 2016
(Magma) [Fibonacci(2*k)*Fibonacci(2*n2*k+1): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 15 2019
(Sage) [[fibonacci(2*k)*fibonacci(2*n2*k+1) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Jul 15 2019
(GAP) Flat(List([1..12], n> List([1..n], k> Fibonacci(2*k)*Fibonacci(2*n2*k+1) ))); # G. C. Greubel, Jul 15 2019


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



