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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n consists of n numbers, first F(2n-1) and last F(2n).

Central numbers: (1,6,40,273,...) = A081016.

Row sums: A001870.

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(n-1) for n>=2, with b(1)=1.

In each row, the difference between neighboring terms is a Fibonacci number.

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly 42:1 (2004), pp. 28-35.

FORMULA

Row n: F(2)F(2n-1), F(4)F(2n-3), ..., 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*n-2*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*n-2*k+1));

tabl(nn) = for(n=1, nn, print(row(n))); \\ Michel Marcus, May 03 2016

(MAGMA) [Fibonacci(2*k)*Fibonacci(2*n-2*k+1): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 15 2019

(Sage) [[fibonacci(2*k)*fibonacci(2*n-2*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*n-2*k+1) ))); # G. C. Greubel, Jul 15 2019

CROSSREFS

Cf. A000045, A094566, A094568.

Sequence in context: A331865 A087360 A111501 * A034722 A144712 A050028

Adjacent sequences:  A094562 A094563 A094564 * A094566 A094567 A094568

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, May 12 2004

STATUS

approved

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Last modified September 27 17:05 EDT 2021. Contains 347693 sequences. (Running on oeis4.)