OFFSET
0,2
COMMENTS
Same as Pisot sequences E(1, 41), L(1, 41), P(1, 41), T(1, 41). Essentially same as Pisot sequences E(41, 1681), L(41, 1681), P(41, 1681), T(41, 1681). See A008776 for definitions of Pisot sequences.
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 41-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Numbers n such that sigma(41*n) = 41*n + sigma(n). - Jahangeer Kholdi, Nov 23 2013
For n >= 1, also the number of edge covers in the n-necklace graph. - Eric W. Weisstein, Feb 12 2026
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Eric Weisstein's World of Mathematics, Edge Cover.
Eric Weisstein's World of Mathematics, Necklace Graph.
Index entries for linear recurrences with constant coefficients, signature (41).
FORMULA
G.f.: 1/(1-41*x). - Philippe Deléham, Nov 24 2008
a(n) = 41^n; a(n) = 41*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010
E.g.f.: exp(41*x). - Elmo R. Oliveira, Dec 26 2025
MATHEMATICA
41^Range[0, 14] (* Alonso del Arte, Sep 04 2015 *)
NestList[41#&, 1, 20] (* Harvey P. Dale, Mar 07 2017 *)
PROG
(Magma)[41^n: n in [0..20]]; // Vincenzo Librandi, Nov 21 2010
(PARI) first(m)=vector(m, i, i--; 41^i) \\ Anders Hellström, Sep 12 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved