0,2

Same as Pisot sequences E(1,5), L(1,5), P(1,5), T(1,5). See A008776 for definitions of Pisot sequences.

a(n) has leading digit 1 iff n = A067497 - 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2002

With interpolated zeros 0,1,0,5,0,25,... (G.f.: x/(1-5x^2)) second inverse binomial transform of Fib(3n)/F(3) (A001076). Binomial transform is A085449. - Paul Barry (pbarry(AT)wit.ie), Mar 14 2004

Sums of rows of the triangles in A013620 and A038220. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 14 2006

With a different offset, number of n-permutations (n>=0) of 6 objects: u, v, w, z, x, y with repetition allowed, containing exactly zero (0) or free u's. For example, n=2, a(2)=25 because we have, vv, vw, vz, vx, vy, wv, ww, wz, wx, wy, zv, zw, zz, zx, zy, xv, xw, xz, xx, xy, yv, yw, yz, yx and yy. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 15 2008

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 270

Tanya Khovanova, Recursive Sequences

S. 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.

S. 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.

Eric Weisstein's World of Mathematics, Box Fractal

Index entries for sequences related to linear recurrences with constant coefficients

a(n) = 5^n; a(n) = 5a(n-1).

G.f.: 1/(1-5x), e.g.f.: exp(5x)

[ seq(5^n, n=0..30) ];

A000351:=-1/(-1+5*z); [S. Plouffe in his 1992 dissertation.]

with(finance):seq(futurevalue(1, 4, n), n=0..25); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]

Table[5^n, {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006

(Other) sage: [lucas_number1(n, 5, 0) for n in xrange(1, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

a(n) = A006495(n)^2 + A006496(n)^2.

a(n) = A159991(n)/A001021(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]

Sequence in context: A129066 A102169 A060391 this_sequence A050735 A083590 A097680

Adjacent sequences: A000348 A000349 A000350 this_sequence A000352 A000353 A000354

easy,nonn,nice

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

Removed attribute "conjectured" from Plouffe g.f R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 11 2009