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 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

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