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A165988 First trisection of A022998. 6
0, 3, 12, 9, 24, 15, 36, 21, 48, 27, 60, 33, 72, 39, 84, 45, 96, 51, 108, 57, 120, 63, 132, 69, 144, 75, 156, 81, 168, 87, 180, 93, 192, 99, 204, 105, 216, 111, 228, 117, 240, 123, 252, 129, 264, 135, 276, 141, 288, 147, 300, 153, 312, 159, 324, 165, 336, 171, 348, 177 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Read modulo 10, this yields a sequence with a period of length 10 containing all 10 digits: 0, 3, 2, 9, 4, 5, 6, 1, 8, 7.
The other two trisections start 1, 8, 7, 20, 13, 32, 19, 44.... and 4, 5, 16, 11, 28, 17, 40, 23....
The Pisano period lengths for reading the sequence modulo m>=1 are 1, 2, 1, 4, 10, 2, 14, 8, 6, 10, 22, 4, 26, 14, 10, 16, 34, 6, 38, 20, 14, 22, 46, 8, 50, 26, 18, 28, 58... - R. J. Mathar, Oct 08 2011
LINKS
FORMULA
a(n) = A022998(3n) = 3*A022998(n) = 3*n*(3 +(-1)^n)/2 .
a(n) = 2*a(n-2) - a(n-4).
G.f.: 3*x*(1+4*x+x^2)/((x-1)^2 *(1+x)^2).
E.g.f.: 3*x*(-1 + 3*exp(2*x))*exp(-x)/2. - Ilya Gutkovskiy, Apr 21 2016
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {0, 3, 12, 9}, 50] (* G. C. Greubel, Apr 20 2016 *)
PROG
(PARI) a(n) = my(n=3*n); if (n % 2, n, 2*n); \\ Michel Marcus, Apr 21 2016
CROSSREFS
Sequence in context: A239932 A114237 A060035 * A298028 A215842 A018876
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 03 2009
STATUS
approved

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Last modified April 21 01:42 EDT 2024. Contains 371850 sequences. (Running on oeis4.)