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A226044 Period of length 8: 1, 64, 16, 64, 4, 64, 16, 64. 2
1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64, 1, 64, 16, 64, 4, 64, 16, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A002378(n)/A016754(n) gives 0/1, 2/9, 6/25, 12/49, 20/81, 30/121, 42/169, 56/225,..., where A016754(n) = 4*A002378(n) + 1;

A142705(n)/A154615(n+1) gives 0/1, 3/16,  2/9,  15/64,  6/25,  35/144, 12/49,  63/256,..., where A142705(n) = 4*A154615(n+1) + A010685(n);

A061037(n)/A061038(n) gives 0/1, 5/36,  3/16, 21/100, 2/9,   45/196, 15/64,  77/324,..., where A061038(n) = 4*A061037(n) + A177499(n);

A225948(n)/A226008(n) gives 0/1, 9/100, 5/36, 33/196, 3/16,  65/324, 21/100, 105/484,..., where A226008(n) = 4*A225948(n) + a(n).

See also the triangle in Example lines.

LINKS

Table of n, a(n) for n=0..55.

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

FORMULA

a(n) = A205383(n+7)^2.

G.f.: (1+64*x+16*x^2+64*x^3+4*x^4+64*x^5+16*x^6+64*x^7)/((1-x)*(1+x)*(1+x^2)*(1+x^4)). [Bruno Berselli, May 25 2013]

EXAMPLE

Triangle in which the terms of each line are repeated:

A000012: 1,   ...

A010685: 1,   4,  ...

A177499: 1,  16,  4,  16,  ...

A226044: 1,  64, 16,  64,  4,  64, 16,  64, ...

         1, 256, 64, 256, 16, 256, 64, 256, 4, 256, 64, 256, 16, 256, 64, 256, ...

MATHEMATICA

Table[{1, 64, 16, 64, 4, 64, 16, 64}, {7}] // Flatten (* Jean-Fran├žois Alcover, May 24 2013 *)

CROSSREFS

Cf. A010685, A177499, A205383, A225948.

Sequence in context: A298923 A210114 A236179 * A065790 A147792 A304229

Adjacent sequences:  A226041 A226042 A226043 * A226045 A226046 A226047

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, May 24 2013

STATUS

approved

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)