A008706 Coordination sequence for 3.3.3.4.4 planar net.

1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275

Offset

0,2

Comments

Also the Engel expansion of exp^(1/5); cf. A006784 for the Engel expansion definition. - Benoit Cloitre, Mar 03 2002

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Brian Galebach, k-uniform tilings (k <= 6) and their A-numbers

Chaim Goodman-Strauss and N. J. A. Sloane, A Coloring Book Approach to Finding Coordination Sequences, Acta Cryst. A75 (2019), 121-134, also on NJAS's home page. Also arXiv:1803.08530.

Branko Grünbaum and Geoffrey C. Shephard, Tilings by regular polygons, Mathematics Magazine, 50 (1977), 227-247.

Tom Karzes, Tiling Coordination Sequences

Reticular Chemistry Structure Resource, cem

N. J. A. Sloane, The uniform planar nets and their A-numbers [Annotated scanned figure from Gruenbaum and Shephard (1977)]

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

From Paul Barry, Jul 21 2003: (Start)

G.f.: (1 + 3*x + x^2)/(1 - x)^2.

a(n) = 0^n + 5n. (End)

G.f.: A(x) + 1, where A(x) is the g.f. of A008587. - Gennady Eremin, Feb 21 2021

E.g.f.: 1 + 5*x*exp(x). - Stefano Spezia, Jan 05 2023

Example

G.f. = 1 + 5*x + 10*x^2 + 15*x^3 + 20*x^4 + 25*x^5 + 30*x^6 + 35*x^7 + ...

Mathematica

Join[{1}, LinearRecurrence[{2, -1}, {5, 10}, 100]] (* Jean-François Alcover, Dec 13 2018 *)

Prog

(Magma) [0^n+5*n: n in [0..50] ]; // Vincenzo Librandi, Aug 21 2011
(PARI) a(n)=0^n+5*n \\ Charles R Greathouse IV, Mar 19 2015

Crossrefs

Cf. A006784, A048476 (binomial Transf.)

Essentially the same as A008587.

List of coordination sequences for uniform planar nets: A008458 (the planar net 3.3.3.3.3.3), A008486 (6^3), A008574 (4.4.4.4 and 3.4.6.4), A008576 (4.8.8), A008579 (3.6.3.6), A008706 (3.3.3.4.4), A072154 (4.6.12), A219529 (3.3.4.3.4), A250120 (3.3.3.3.6), A250122 (3.12.12).

First differences of A005891.

Sequence in context: A350744 A248359 A008587 * A172336 A140233 A172328

Adjacent sequences: A008703 A008704 A008705 * A008707 A008708 A008709

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved