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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007754 Array (a frieze pattern) defined by a(n,k) = (a(n-1,k)*a(n-1,k+1) - 1) / a(n-2,k+1), read by antidiagonals. 12
1, 1, 1, 1, 2, 1, 1, 3, 5, 2, 1, 4, 11, 18, 7, 1, 5, 19, 52, 85, 33, 1, 6, 29, 110, 301, 492, 191, 1, 7, 41, 198, 751, 2055, 3359, 1304, 1, 8, 55, 322, 1555, 5898, 16139, 26380, 10241, 1, 9, 71, 488, 2857, 13797, 52331, 143196, 234061, 90865, 1, 10, 89, 702 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Let u be a sequence with u(0)=p, u(1)=q, and u(i)^(i+k) = u(i-1)*u(i+1). Then u(n)= q^a(n-1,k)/p^a(n-2,k+1). - Example for k=1, u(5)=q^7/p^18 and for k=2, u(5)=q^85/p^52. - Olivier Gérard, Sep 19 2016

REFERENCES

Email from James Propp, Nov 28 2000.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

FORMULA

a(n, k) = (n+k)*a(n-1, k)-a(n-2, k) with a(0, k)=1 and a(-1, k)=0. - Henry Bottomley, Feb 28 2001

a(n, k) = Pi*(BesselJ(n+k+1, 2)*BesselY(k, 2) - BesselY(n+k+1, 2)*BesselJ(k, 2)). - Alec Mihailovs (alec(AT)mihailovs.com), Aug 21 2005

Column asymptotics (i.e. for fixed k and n -> infinity): a(n, k) ~ BesselJ(k, 2)*(n+k)!. - Alec Mihailovs (alec(AT)mihailovs.com), Aug 21 2005

EXAMPLE

Array begins:

  1  1   1   1   1  1 1 1 ...

  1  2   3   4   5  6 7 ...

  1  5  11  19  29 41 ...

  2 18  52 110 198 ...

  7 85 301 751 ...

CROSSREFS

Row 0-3: A000012, A000027(n+1), A028387, A058794-A058796. Columns 0-2: A058797-A058799.

Sequence in context: A090234 A286380 A275866 * A144866 A058732 A060082

Adjacent sequences:  A007751 A007752 A007753 * A007755 A007756 A007757

KEYWORD

nonn,easy,nice,tabl

AUTHOR

N. J. A. Sloane, Nov 28 2000

EXTENSIONS

More terms from Christian G. Bower, Dec 02 2000

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 01:27 EDT 2019. Contains 325228 sequences. (Running on oeis4.)