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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

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Cf. A165351, A165355, A165367.

Sequence in context: A239932 A114237 A060035 * A298028 A215842 A018876

Adjacent sequences:  A165985 A165986 A165987 * A165989 A165990 A165991

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Oct 03 2009

EXTENSIONS

Extended by R. J. Mathar, Oct 05 2009

STATUS

approved

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Last modified February 19 03:25 EST 2018. Contains 299330 sequences. (Running on oeis4.)