The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 * A364122 A034722 A144712 Adjacent sequences: A094562 A094563 A094564 * A094566 A094567 A094568 KEYWORD nonn,tabl AUTHOR Clark Kimberling, May 12 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 12 10:07 EDT 2024. Contains 373329 sequences. (Running on oeis4.)