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A152929
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.
48
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
OFFSET
1,1
LINKS
S. Schlicker, L. Morales, and 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.
FORMULA
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
a(n) = a(n-1) + a(n-2) for n>2. - Colin Barker, Aug 05 2020
a(n) = Lucas(n+9) - Fibonacci(n+6) - Fibonacci(n-5). - Greg Dresden, Mar 14 2022
MAPLE
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
MATHEMATICA
LinearRecurrence[{1, 1}, {113, 176}, 50] (* Paolo Xausa, Jul 23 2024 *)
PROG
(PARI) A152929(n)=50*fibonacci(n)+63*fibonacci(n+1) \\ M. F. Hasler, Apr 14 2015
(PARI) Vec(x*(113 + 63*x) / (1 - x - x^2) + O(x^30)) \\ Colin Barker, Aug 05 2020
KEYWORD
nonn,easy
AUTHOR
Steven Schlicker, Dec 15 2008
EXTENSIONS
More terms from M. F. Hasler, Apr 16 2015
STATUS
approved