A001020 Powers of 11: a(n) = 11^n. (Formerly M4807 N2054)

1, 11, 121, 1331, 14641, 161051, 1771561, 19487171, 214358881, 2357947691, 25937424601, 285311670611, 3138428376721, 34522712143931, 379749833583241, 4177248169415651, 45949729863572161, 505447028499293771, 5559917313492231481, 61159090448414546291

Offset

0,2

Comments

Same as Pisot sequences E(1, 11), L(1, 11), P(1, 11), T(1, 11). Essentially same as Pisot sequences E(11, 121), L(11, 121), P(11, 121), T(11, 121). 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 11-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

a(n), for n <= 4, gives the n-th row of Pascal's triangle (A007318); a(n), n >= 5 "sort of" gives the n-th row of Pascal's triangle, but now the binomial coefficients with more than one digit overlap. - Daniel Forgues, Aug 12 2012

Numbers n such that sigma(11*n) = 11*n + sigma(n). - Jahangeer Kholdi, Nov 13 2013

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..100

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 275

Tanya Khovanova, Recursive Sequences

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

Index entries for linear recurrences with constant coefficients, signature (11).

Formula

G.f.: 1/(1-11*x).

E.g.f.: exp(11*x).

a(n) = 11*a(n-1), n > 0; a(0)=1. - Philippe Deléham, Nov 23 2008

Maple

A001020:=-1/(-1+11*z); # Simon Plouffe in his 1992 dissertation

Mathematica

Table[11^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

Prog

(Magma) [11^n: n in [0..100]]; // Vincenzo Librandi, Apr 24 2011
(Maxima) makelist(11*n, n, 0, 20); /* Martin Ettl, Dec 17 2012 */
(PARI) a(n)=n^11 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A096884, A097659, A007318.

Sequence in context: A045587 A059734 A045582 * A325203 A055479 A195946

Adjacent sequences: A001017 A001018 A001019 * A001021 A001022 A001023

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved