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A152929
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Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two 4-gonal polygonal components chained with string components of length l as l varies.
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9
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113, 176, 289, 465, 754, 1219, 1973, 3192, 5165, 8357, 13522, 21879, 35401, 57280, 92681, 149961, 242642, 392603, 635245, 1027848, 1663093, 2690941, 4354034, 7044975, 11399009, 18443984, 29842993, 48286977, 78129970, 126416947, 204546917, 330963864, 535510781, 866474645
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..34.
S. Schlicker, L. Morales, D. Schultheis, Polygonal chain sequences in the space of compact sets, J. Integer Seq. 12 (2009), no. 1, Article 09.1.7, 23 pp.
P. E. Weidmann, The OEIS Sequencer survey, Apr 11 2015
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FORMULA
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a(n) = (163*A000045(n)+63*A000032(n))/2. - Conjectured by Philipp Emanuel Weidmann, cf. LINKS.
G.f.: x*(113 + 63*x)/(1 - x - x^2). - M. F. Hasler, Apr 16 2015
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MAPLE
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with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L4, Q: F := fibonacci: L4 := F(3)+F(5): aa := L4*F(n-2)+F(6)*F(n-1): b := L4*F(n-1)+F(6)*F(n): c := F(6)*F(n-2)+F(4)^2*F(n-1): d := F(6)*F(n-1)+F(4)^2*F(n): Q := sqrt((d-aa)^2+4*b*c); lambda := (d+aa+Q)/2: delta := (d+aa-Q)/2: R := ((lambda-d)*L4+b*F(6))/Q: S := ((lambda-aa)*L4-b*F(6))/Q: simplify(R*lambda+S*delta); end proc: # Simplified by M. F. Hasler, Apr 16 2015
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PROG
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(PARI) A152929(n)==50*fibonacci(n)+63*fibonacci(n+1) \\ M. F. Hasler, Apr 14 2015
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CROSSREFS
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Cf. A152927, A152928, A152930, A152931, A152932, A152933, A152934, A152935.
Sequence in context: A167631 A264778 A142303 * A142180 A325084 A084951
Adjacent sequences: A152926 A152927 A152928 * A152930 A152931 A152932
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KEYWORD
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nonn
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AUTHOR
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Steven Schlicker (schlicks(AT)gvsu.edu), Dec 15 2008
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EXTENSIONS
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More terms from M. F. Hasler, Apr 16 2015
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STATUS
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approved
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