A165988 First trisection of A022998.

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

Author

Paul Curtz, Oct 03 2009

Keywords

• nonn
• easy

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
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A165351, A165355, A165367.

Programs

Mathematica

LinearRecurrence[{0, 2, 0, -1}, {0, 3, 12, 9}, 50] (* G. C. Greubel, Apr 20 2016 *)

PARI

a(n) = my(n=3*n); if (n % 2, n, 2*n); \\ Michel Marcus, Apr 21 2016

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