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

1,1

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).

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

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

Crossrefs

Cf. A000032, A000045.

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

Keyword

nonn,easy

Author

Steven Schlicker, Dec 15 2008

Extensions

More terms from M. F. Hasler, Apr 16 2015

Status

approved