login
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
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
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 03 2009
STATUS
approved