A152939 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of four 4-gonal polygonal components chained with string components of length l as l varies.

29153, 109649, 486385, 2024613, 8634049, 36481021, 154687133, 655020765, 2775107981, 11754906113, 49795616797, 210935942361, 893541701545, 3785099002297, 16033943772281, 67920864283629, 287717416776137, 1218790505711045, 5162879481166789, 21870308363154597

Offset

1,1

Links

Table of n, a(n) for n=1..20.

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.

Formula

Conjectures from Colin Barker, Jul 09 2020: (Start)

G.f.: x*(29153 + 22190*x - 17480*x^2 - 4977*x^3) / ((1 + x - x^2)*(1 - 4*x - x^2)).

a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4) for n>4.

(End)

Maple

with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, R, S, F, L, k, m: k:=4: m:=2: F := t -> fibonacci(t): L := t -> fibonacci(t-1)+fibonacci(t+1): aa := (m, n) -> L(2*m)*F(n-2)+F(2*m+2)*F(n-1): b := (m, n) -> L(2*m)*F(n-1)+F(2*m+2)*F(n): c := (m, n) -> F(2*m+2)*F(n-2)+F(m+2)^2*F(n-1): d := (m, n) -> F(2*m+2)*F(n-1)+F(m+2)^2*F(n): lambda := (m, n) -> (d(m, n)+aa(m, n)+sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): delta := (m, n) -> (d(m, n)+aa(m, n)-sqrt((d(m, n)-aa(m, n))^2+4*b(m, n)*c(m, n)))*(1/2): R := (m, n) -> ((lambda(m, n)-d(m, n))*L(2*m)+b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): S := (m, n) -> ((lambda(m, n)-aa(m, n))*L(2*m)-b(m, n)*F(2*m+2))/(2*lambda(m, n)-d(m, n)-aa(m, n)): simplify(R(m, n)*lambda(m, n)^(k-1)+S(m, n)*delta(m, n)^(k-1)); end proc;

Crossrefs

Cf. A152927, A152928, A152929, A152930, A152931, A152932, A152933, A152934.

Sequence in context: A257391 A015313 A242741 * A028462 A357272 A252860

Adjacent sequences: A152936 A152937 A152938 * A152940 A152941 A152942

Keyword

nonn

Author

Steven Schlicker, Dec 15 2008

Status

approved