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A001020
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Powers of 11.
(Formerly M4807 N2054)
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32
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1, 11, 121, 1331, 14641, 161051, 1771561, 19487171, 214358881, 2357947691, 25937424601, 285311670611, 3138428376721, 34522712143931, 379749833583241, 4177248169415651, 45949729863572161, 505447028499293771, 5559917313492231481, 61159090448414546291
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OFFSET
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0,2
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COMMENTS
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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 Pascals' triangle (A007318); a(n), n >= 5 "sort of" gives the n-th row of Pascals' triangle, but now the binomial coefficients with more than one digit overlap. - Daniel Forgues, Aug 12 2012
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REFERENCES
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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).
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LINKS
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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 S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
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G.f.: 1/(1-11*x).
E.g.f.: exp(11*x).
a(n) = 11*a(n-1), n>0 ; a(0)=1 . [Philippe DELEHAM, Nov 23 2008]
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MAPLE
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A001020:=-1/(-1+11*z); [Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[11^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
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PROG
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(MAGMA) [11^n: n in [0..100]]; // Vincenzo Librandi, Apr 24 2011
(Maxima) makelist(11*n, n, 0, 20); /* Martin Ettl, Dec 17 2012 */
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CROSSREFS
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Cf. A096884, A097659, A007318.
Sequence in context: A045587 A059734 A045582 * A055479 A195946 A003590
Adjacent sequences: A001017 A001018 A001019 * A001021 A001022 A001023
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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