login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202452 Lower triangular Fibonacci matrix, by SW antidiagonals. 4
1, 1, 0, 2, 1, 0, 3, 1, 0, 0, 5, 2, 1, 0, 0, 8, 3, 1, 0, 0, 0, 13, 5, 2, 1, 0, 0, 0, 21, 8, 3, 1, 0, 0, 0, 0, 34, 13, 5, 2, 1, 0, 0, 0, 0, 55, 21, 8, 3, 1, 0, 0, 0, 0, 0, 89, 34, 13, 5, 2, 1, 0, 0, 0, 0, 0, 144, 55, 21, 8, 3, 1, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

C. Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195-202.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

Column n consists of n-1 zeros followed by the Fibonacci sequence (1,1,2,3,5,8,...).

EXAMPLE

Northwest corner:

1...0...0...0...0...0...0...0...0

1...1...0...0...0...0...0...0...0

2...1...1...0...0...0...0...0...0

3...2...1...1...0...0...0...0...0

5...3...2...1...1...0...0...0...0

MATHEMATICA

n = 12;

Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];

P = Transpose[Q]; F = P.Q;

Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202451 as a sequence *)

Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202452 as a sequence *)

Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n}, {i, 1, k}]] (* A202453 as a sequence *)

TableForm[Q]  (* A202451, upper triangular Fibonacci array *)

TableForm[P]  (* A202452, lower triangular Fibonacci array *)

TableForm[F]  (* A202453, Fibonacci self-fusion matrix *)

TableForm[FactorInteger[F]]

CROSSREFS

Cf. A202451, A202453, A202462, A188516, A000045.

Sequence in context: A063173 A120111 A130055 * A127013 A117362 A247492

Adjacent sequences:  A202449 A202450 A202451 * A202453 A202454 A202455

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 19 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 06:24 EST 2017. Contains 295868 sequences.