OFFSET
0,2
COMMENTS
Also the Engel expansion of exp^(1/5); cf.A006784for 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, alsoon NJAS's home page.AlsoarXiv: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
FromPaul 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. ofA008587.-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 asA008587.
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 ofA005891.
KEYWORD
nonn,easy
AUTHOR
STATUS
approved