A323260 Number of horizontally convex polyoctagons containing n regular polygons (squares or octagons).

0, 2, 6, 24, 96, 390, 1582, 6422, 26062, 105768, 429228, 1741898, 7068978, 28687370, 116419254, 472453328, 1917312976, 7780851238, 31576298030, 128143125598, 520031215214, 2110393854816, 8564413235420, 34756154117738, 141047636989250, 572400382184434, 2322918728158854, 9426882974883464

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

K. A. Van'kov, V. M. Zhuravlyov, Regular tilings and generating functions, Mat. Pros. Ser. 3, issue 22, 2018 (127-157) [in Russian]. See Table 1, g_n.

Index entries for linear recurrences with constant coefficients, signature (5,-3,-5,7,-1).

Formula

G.f. = 2*x*(1-x)^3*(1+x)/(1-5*x+3*x^2+5*x^3-7*x^4+x^5).

a(n) = 2*A323261(n).

a(n) = 5*a(n-1) - 3*a(n-2) - 5*a(n-3) + 7*a(n-4) - a(n-5) for n>5. - Colin Barker, Jan 10 2019

Mathematica

CoefficientList[Series[2*x*(1-x)^3*(1+x)/(1-5*x+3*x^2+5*x^3-7*x^4+x^5), {x, 0, 27}], x] (* Amiram Eldar, Jan 10 2019 *)

Prog

(PARI) concat(0, Vec(2*x*(1 - x)^3*(1 + x) / (1 - 5*x + 3*x^2 + 5*x^3 - 7*x^4 + x^5) + O(x^30))) \\ Colin Barker, Jan 10 2019

Crossrefs

Cf. A323261-A323269.

Sequence in context: A179363 A084509 A334767 * A147915 A147906 A147898

Adjacent sequences: A323257 A323258 A323259 * A323261 A323262 A323263

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 09 2019

Status

approved