A010709 Constant sequence: the all 4's sequence.

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

0,1

Comments

From Klaus Brockhaus, May 25 2010: (Start)

Continued fraction expansion of 2+sqrt(5).

Decimal expansion of 4/9.

Inverse binomial transform of A020707. (End)

Links

Table of n, a(n) for n=0..104.

Tom Edgar, Proof without words: sum of powers of 4/9, Math. Mag. 89 no. 3 (2016) 191.

Tanya Khovanova, Recursive Sequences

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1012

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

From Klaus Brockhaus, May 25 2010: (Start)

a(n) = 4.

G.f.: 4/(1-x). (End)

E.g.f.: 4*e^x. - Vincenzo Librandi, Jan 29 2012

Prog

(PARI) a(n) = 4 \\ Charles R Greathouse IV, Apr 07 2012
(Maxima) makelist(4, n, 0, 30); /* Martin Ettl, Nov 09 2012 */
(Python)
def A010709(n): return 4 # Chai Wah Wu, Mar 22 2023

Crossrefs

From Klaus Brockhaus, May 25 2010: (Start)

Equals 4*A000012, 2*A007395, A010731/2, A010855/4, A010871/8.

Cf. A098317 (decimal expansion of 2+sqrt(5)), A020707 (2^(n+2)). (End)

Sequence in context: A088849 A251539 A123932 * A138908 A032564 A141248

Adjacent sequences: A010706 A010707 A010708 * A010710 A010711 A010712

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved