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.
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
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- 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.
- Index entries for linear recurrences with constant coefficients, signature (1,1).
Crossrefs
Programs
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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
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Mathematica
LinearRecurrence[{1, 1}, {113, 176}, 50] (* Paolo Xausa, Jul 23 2024 *) -
PARI
A152929(n)=50*fibonacci(n)+63*fibonacci(n+1) \\ M. F. Hasler, Apr 14 2015
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PARI
Vec(x*(113 + 63*x) / (1 - x - x^2) + O(x^30)) \\ Colin Barker, Aug 05 2020
Formula
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
Extensions
More terms from M. F. Hasler, Apr 16 2015