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A007754
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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.
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10
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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; internal format)
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OFFSET
| 0,5
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REFERENCES
| Email from James Propp (propp(AT)math.wisc.edu), Nov. 28, 2000.
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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 (se16(AT)btinternet.com), 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
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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 ...
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CROSSREFS
| Row 0-3: A000012, A000027(n+1), A028387, A058794-A058796. Columns 0-2: A058797-A058799.
Sequence in context: A114163 A189435 A090234 * A144866 A058732 A060082
Adjacent sequences: A007751 A007752 A007753 * A007755 A007756 A007757
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KEYWORD
| nonn,easy,nice,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2000
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net), Dec 02 2000
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