A010871 -id:A010871 - cp's OEIS frontend

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

N. J. A. Sloane

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)

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).

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)

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

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

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

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

A174927 Periodic sequence: Repeat 1, 64.

Original entry on oeis.org

1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64

Offset: 0

Klaus Brockhaus, Apr 02 2010

Interleaving of A000012 and 2*A010871.
Also continued fraction expansion of (4+sqrt(17))/8.
First differences of A174928.

Index entries for linear recurrences with constant coefficients, signature (0, 1).

Cf. A000012 (all 1's sequence), A010871 (all 32's sequence), A010689 (repeat 1, 8), A174930 (decimal expansion of (4+sqrt(17))/8), A174928.

&cat[ [1, 64]: n in [0..41] ];
[ (65-63*(-1)^n)/2: n in [0..83] ];

PadRight[{},100,{1,64}] (* Harvey P. Dale, Jun 16 2013 *)

a(n) = (65-63*(-1)^n)/2.
a(n) = a(n-2) for n > 1; a(0) = 0, a(1) = 64.
a(n) = -a(n-1)+65 for n > 0; a(0) = 1.
a(n) = ((n+1) mod 2)+64*(n mod 2).
G.f.: (1+64*x)/((1-x)*(1+x)).

cp's OEIS Frontend

A010709 Constant sequence: the all 4's sequence.

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