A138635 a(n) =3*a(n-3)-3*a(n-6)+2*a(n-9).

0, 0, 1, 0, 1, 1, 1, 2, 1, 3, 3, 2, 6, 5, 5, 11, 10, 11, 21, 21, 22, 42, 43, 43, 85, 86, 85, 171, 171, 170, 342, 341, 341, 683, 682, 683, 1365, 1365, 1366, 2730, 2731, 2731, 5461, 5462, 5461, 10923, 10923, 10922, 21846, 21845, 21845, 43691, 43690, 43691, 87381

Offset

0,8

Comments

As the recurrence shows, these are three interleaved sequences which obey recurrences b(n)=3*b(n-1)-3*b(n-2)+2*b(n-3), indicating that the b(n) equal their third differences.

These three sequences are A024495, A024494 (or A131708) and A024493 (or A130781).

Their starting "vectors" b(0,1,2) are 0,0,1 and 0,1,2 and 1,1,1, respectively, therefore linearly independent, such that other sequences with the same recursion as b(n) can be written as linear combinations of these.

Links

Table of n, a(n) for n=0..54.

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,2).

Formula

a(18*n) = 21*A133853(n).

G.f.: -x^2*(1+x^2-2*x^3+x^4-x^5+x^6)/((2*x^3-1)*(x^6-x^3+1)). - R. J. Mathar, May 17 2009

Crossrefs

Cf. A024493, A024494, A024495, A131708, A130781.

Sequence in context: A210864 A349550 A144305 * A128182 A059739 A035566

Adjacent sequences: A138632 A138633 A138634 * A138636 A138637 A138638

Keyword

nonn,easy

Author

Paul Curtz, May 14 2008

Extensions

Edited by R. J. Mathar, May 17 2009

Status

approved