login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A349550 Meta-Wythoff array based on A097285: M = (M(n,k)), by downward antidiagonals; every row of M is eventually a row of the Wythoff array, W = A035513, and every row of W is a row of M; see Comments. 1
1, 2, 1, 3, 3, 2, 5, 4, 3, 1, 8, 7, 5, 4, 2, 13, 11, 8, 5, 4, 3, 21, 18, 13, 9, 6, 4, 1, 34, 29, 21, 14, 10, 7, 5, 2, 55, 47, 34, 23, 16, 11, 6, 5, 3, 89, 76, 55, 37, 26, 18, 11, 7, 5, 4, 144, 123, 89, 60, 42, 29, 17, 12, 8, 5, 1, 233, 199, 144, 97, 68, 47 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Suppose that (s(1), s(2), ...) is a sequence satisfying s(k) = s(k-1) + s(k-2) for k >= 3. If s(1) and s(2) are positive integers, then there is an index n such that (s(n), s(n+1), ...) is a row of A035513. The n-th row of M is the sequence (s(1), s(2), ...), where (s(1), s(2)) are the n-th pair described in A097285.

Every row of W is a row of M; indeed, M consists of all tails of all rows of W.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

Corner:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

1, 4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411

2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466

3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521

1, 5, 6, 11, 17, 28, 45, 73, 118, 191, 309, 500

2, 5, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555

3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610

4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411, 665

Example: The first 7 pairs in A097285 are (1,2), (1,3), (2,3), (1,4), (2,4), (3,4), (1,5), so that the first 7 rows of M are

(1,2,3,5,8,...) = (row 1 of W) = Fibonacci numbers, A000045;

(1,3 4,7,11,...), which includes row 2 of W, the Lucas numbers, A000032;

(2,3,5,8,13,...), a tail of row 1 of W;

(1,4,5,9,14,...), which includes row 4 of W;

(2,4,6,10,16,...), which includes row 3 of W;

(3,4,7,11,18,...), which includes row 2 of W;

(1,5,6,11,17,...), which includes row 7 of W.

MATHEMATICA

z1 = 30; zc = 20; zr = 20;

t1 = {1, 2}; Do[t1 = Join[t1, Riffle[Range[n - 1], n], {n}], {n, 3, z1}]; (* A097285 *)

t = Partition[t1, 2];

f[n_] := Fibonacci[n]; r = (1 + Sqrt[5])/2;

s[h_, k_] := Table[h*f[n - 1] + k*f[n], {n, 2, zc}];

w = Table[Join[{h = t[[n]][[1]], k = t[[n]][[2]]}, s[h, k]], {n, 1, zr}]

TableForm[w] (* A349550 array *)

w1[n_, k_] := w[[n]][[k]];

Table[w1[n - k + 1, k], {n, 13}, {k, n, 1, -1}] // Flatten (* A349550 sequence *)

CROSSREFS

Cf. A000032, A000045, A035513, A097285, A349551, A349552, A349553, A349554.

Sequence in context: A111492 A319254 A210864 * A144305 A138635 A128182

Adjacent sequences: A349547 A349548 A349549 * A349551 A349552 A349553

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Nov 21 2021

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 06:18 EST 2022. Contains 358431 sequences. (Running on oeis4.)