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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202869 Symmetric matrix based on the lower Wythoff sequence, A000201, by antidiagonals. 3
1, 3, 3, 4, 10, 4, 6, 15, 15, 6, 8, 22, 26, 22, 8, 9, 30, 39, 39, 30, 9, 11, 35, 54, 62, 54, 35, 11, 12, 42, 66, 87, 87, 66, 42, 12, 14, 47, 79, 108, 126, 108, 79, 47, 14, 16, 54, 90, 132, 159, 159, 132, 90, 54, 16, 17, 62, 103, 151, 196, 207, 196, 151, 103, 62 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let s=(1,3,4,6,8,...)=A000201) and let T be the infinite square matrix whose n-th row is formed by putting n-1 zeros before the terms of s.  Let T' be the transpose of T.  Then A202869 represents the matrix product M=T'*T.  M is the self-fusion matrix of s, as defined at A193722.  See A202870 for characteristic polynomials of principal submatrices of M,with interlacing zeros.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

Northwest corner:

1...3....4....6....8....9

3...10...15...22...30...35

4...15...26...39...54...66

6...22...39...62...87...108

8...30...54...87...126..159

MATHEMATICA

s[k_] := Floor[k*GoldenRatio];

U = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[s[k], {k, 1, 15}]];

L = Transpose[U]; M = L.U; TableForm[M]

m[i_, j_] := M[[i]][[j]];

Flatten[Table[m[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]]

f[n_] := Sum[m[i, n], {i, 1, n}] + Sum[m[n, j], {j, 1, n - 1}]

Table[f[n], {n, 1, 12}]

Table[Sqrt[f[n]], {n, 1, 12}]   (* A054347 *)

Table[m[1, j], {j, 1, 12}]        (* A000201 *)

CROSSREFS

Cf. A202870.

Sequence in context: A130626 A175796 A115284 * A202871 A144626 A033707

Adjacent sequences:  A202866 A202867 A202868 * A202870 A202871 A202872

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 26 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 01:18 EST 2016. Contains 279033 sequences.