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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. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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

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

CROSSREFS

Cf. A152927, A152928, A152930, A152931, A152932, A152933, A152934, A152935.

Sequence in context: A167631 A264778 A142303 * A142180 A084951 A151947

Adjacent sequences:  A152926 A152927 A152928 * A152930 A152931 A152932

KEYWORD

nonn

AUTHOR

Steven Schlicker (schlicks(AT)gvsu.edu), Dec 15 2008

EXTENSIONS

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

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.