0,2

Same as Pisot sequences E(1,8), L(1,8), P(1,8), T(1,8). See A008776 for definitions of Pisot sequences.

If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3} such that for fixed y_1,y_2,...,y_n in {1,2,3} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 24 2007

With a different offset, number of n-permutations (n>=0) of 9 objects: r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly zero (0) or free u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 15 2008

1/1 + 1/8 + 1/64 + 1/512 + 1/4096 + ... = 8/7 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2008]

a(n) = A157176(A008588(n)); a(n+1) = A157176(A016969(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]

This is the auto-convolution (convolution square) of A059304. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 25 2009]

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).

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 273

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Tanya Khovanova, Recursive Sequences

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

Eric Weisstein's World of Mathematics, Sierpinski Carpet

Index entries for sequences related to linear recurrences with constant coefficients

a(n) = 8^n; a(n) = 8a(n-1).

G.f.: 1/(1-8x), e.g.f.: exp(8x)

with(finance):seq(futurevalue(1, 7, n), n=0..20); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]

(Other) sage: [lucas_number1(n, 8, 0) for n in xrange(1, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]

A013730, A103333, A013731, A067417, A083233, A055274. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 24 2009]

Sequence in context: A171282 A125498 A125908 this_sequence A097682 A050738 A046238

Adjacent sequences: A001015 A001016 A001017 this_sequence A001019 A001020 A001021

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).

More terms a(21), a(22), a(23) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2009