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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A291678 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of k-th power of continued fraction 1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + x^5/(1 + ...))))). 3
1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 3, 1, -1, 0, 1, 4, 3, -2, 0, 0, 1, 5, 6, -2, -2, 1, 0, 1, 6, 10, 0, -6, 2, 1, 0, 1, 7, 15, 5, -11, 0, 5, -1, 0, 1, 8, 21, 14, -15, -8, 12, 0, -2, 0, 1, 9, 28, 28, -15, -24, 18, 9, -8, 0, 0, 1, 10, 36, 48, -7, -48, 15, 32, -15, -6, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

G.f. of column k: Product_{j>=1} ((1 - x^(5*j-2))*(1 - x^(5*j-3)) / ((1 - x^(5*j-1))*(1 - x^(5*j-4))))^k.

EXAMPLE

Square array begins:

   1,  1,  1,  1,   1, ...

   0,  1,  2,  3,   4, ...

   0,  0,  1,  3,   6, ...

   0, -1, -2, -2,   0, ...

   0,  0, -2, -6, -11, ...

CROSSREFS

Columns k=0..4 give A000007, A003823, A285442, A285443, A285444.

Rows n=0..1 give A000012, A001477.

Main diagonal gives A291679.

Antidiagonal sums give A302016.

Cf. A286509.

Sequence in context: A291170 A275001 A290975 * A286180 A291701 A286352

Adjacent sequences:  A291675 A291676 A291677 * A291679 A291680 A291681

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, Aug 29 2017

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 August 22 02:02 EDT 2018. Contains 313959 sequences. (Running on oeis4.)