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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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

• 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
• Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (1).

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)

Programs

Maxima

makelist(4, n, 0, 30); /* Martin Ettl, Nov 09 2012 */

PARI

a(n) = 4 \\ Charles R Greathouse IV, Apr 07 2012

Python

def A010709(n): return 4 # Chai Wah Wu, Mar 22 2023

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