OFFSET
0,3
COMMENTS
Also, the number of numbers with at most n digits whose largest digit equals 4. - M. F. Hasler, May 03 2015
a(n) is divisible by 7 iff n is divisible by 6; for example: a(6) = 11529 = 7 * 1647 (see 'Les cahier du bac' or subtract A070365 and A153727 and locate zeros). - Bernard Schott, Oct 02 2020
a(n) is the number of n-digit numbers whose smallest decimal digit is 5. - Stefano Spezia, Nov 15 2023
REFERENCES
Les Cahiers du Bac, Terminales C & E, Tome 1, 1985, Exercice 109, p. 18; Bac Rouen, Série C, 1978.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..200
X. Acloque, Polynexus Numbers and other mathematical wonders [broken link]
Samuele Giraudo, Pluriassociative algebras I: The pluriassociative operad, arXiv:1603.01040 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (9,-20).
FORMULA
a(n) = 5*a(n-1) + 4^(n-1). - Xavier Acloque, Oct 20 2003
From Mohammad K. Azarian, Jan 14 2009: (Start)
G.f.: 1/(1-5*x) - 1/(1-4*x).
E.g.f.: e^(5*x) - e^(4*x). (End)
a(n) = 9*a(n-1) - 20*a(n-2), a(0)=0, a(1)=1. - Vincenzo Librandi, Jan 28 2011
MAPLE
a:=n->sum(4^(n-j)*binomial(n, j), j=1..n): seq(a(n), n=0..18); # Zerinvary Lajos, Jan 04 2007
MATHEMATICA
a[n_]:=5^n-4^n; a[Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
LinearRecurrence[{9, -20}, {0, 1}, 30] (* Harvey P. Dale, Oct 01 2016 *)
PROG
(Sage) [lucas_number1(n, 9, 20) for n in range(21)] # Zerinvary Lajos, Apr 23 2009
(PARI) a(n)=5^n-4^n \\ M. F. Hasler, May 03 2015
(GAP) List([0..20], n->5^n - 4^n); # Muniru A Asiru, Mar 04 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved