|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
