A152928 Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 1 as m varies.

113, 765, 5234, 35865, 245813, 1684818, 11547905, 79150509, 542505650, 3718389033, 25486217573, 174685133970, 1197309720209, 8206482907485, 56248070632178, 385530011517753, 2642462009992085, 18111704058426834, 124139466398995745, 850864560734543373

Offset

2,1

Links

Colin Barker, Table of n, a(n) for n = 2..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.

Index entries for linear recurrences with constant coefficients, signature (8,-8,1).

Formula

G.f.: x^2*(113 - 139*x + 18*x^2)/(1 - 8*x + 8*x^2 - x^3). - M. F. Hasler, Apr 16 2015

a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3) for n>4. - Colin Barker, Aug 05 2020

Maple

with(combinat): a := proc(n) local aa, b, c, d, lambda, delta, Q, F, L:  F := fibonacci: L := t -> fibonacci(t-1)+fibonacci(t+1): aa := L(2*n)*F(l-2)+F(2*n+2)*F(l-1): b := L(2*n)*F(l-1)+F(2*n+2)*F(l): c :=  F(2*n+2)*F(l-2)+F(n+2)^2*F(l-1): d := F(2*n+2)*F(l-1)+F(n+2)^2*F(l): Q:=sqrt((d-aa)^2+4*b*c); lambda := (d+aa+Q)/2: delta := (d+aa-Q)/2: : simplify(lambda*((lambda-d)*L(2*n)+b*F(2*n+2))/Q+delta*((lambda-aa)*L(2*n)-b*F(2*n+2))/Q); end proc; # Simplified by M. F. Hasler, Apr 16 2015

Prog

(PARI) Vec(x^2*(113 - 139*x + 18*x^2) / ((1 - x)*(1 - 7*x + x^2)) + O(x^20)) \\ Colin Barker, Aug 05 2020

Crossrefs

Cf. A152927, A152929, A152930, A152931, A152932, A152933, A152934, A152935.

Sequence in context: A300964 A077287 A087294 * A185337 A365592 A300921

Adjacent sequences: A152925 A152926 A152927 * A152929 A152930 A152931

Keyword

nonn,easy

Author

Steven Schlicker, Dec 15 2008

Extensions

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

Status

approved