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
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.
KEYWORD
nonn,easy
AUTHOR
STATUS
approved