Search: id:A007754
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%I A007754
%S A007754 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,
%T A007754 191,1,7,41,198,751,2055,3359,1304,1,8,55,322,1555,5898,16139,26380,
%U A007754 10241,1,9,71,488,2857,13797,52331,143196,234061,90865,1,10,89,702
%N 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.
%D A007754 Email from James Propp (propp(AT)math.wisc.edu), Nov. 28, 2000.
%F A007754 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 (se16(AT)btinternet.com), Feb 28 2001
%F A007754 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
%F A007754 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
%e A007754 Array begins:
%e A007754 1 1 1 1 1 1 1 1 ...
%e A007754 1 2 3 4 5 6 7 ...
%e A007754 1 5 11 19 29 41 ...
%e A007754 2 18 52 110 198 ...
%e A007754 7 85 301 751 ...
%Y A007754 Row 0-3: A000012, A000027(n+1), A028387, A058794-A058796. Columns 0-2: 
               A058797-A058799.
%Y A007754 Sequence in context: A123352 A114163 A090234 this_sequence A144866 A058732 
               A060082
%Y A007754 Adjacent sequences: A007751 A007752 A007753 this_sequence A007755 A007756 
               A007757
%K A007754 nonn,easy,nice,tabl
%O A007754 0,5
%A A007754 N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2000
%E A007754 More terms from Christian G. Bower (bowerc(AT)usa.net), Dec 02 2000

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