A270810 Expansion of (x - x^2 + 2*x^3 + 2*x^4)/(1 - 3*x + 2*x^2).

0, 1, 2, 6, 16, 36, 76, 156, 316, 636, 1276, 2556, 5116, 10236, 20476, 40956, 81916, 163836, 327676, 655356, 1310716, 2621436, 5242876, 10485756, 20971516, 41943036, 83886076, 167772156, 335544316, 671088636, 1342177276, 2684354556, 5368709116, 10737418236, 21474836476

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

M. Diepenbroek, M. Maus, A. Stoll, Pattern Avoidance in Reverse Double Lists, Preprint 2015. See Table 3.

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

Formula

G.f.: x*(1 - x + 2*x^2 + 2*x^3)/((1 - x)*(1 - 2*x)).

a(n) = 5*2^(n-2)-4 for n>2. - Bruno Berselli, Apr 08 2016

a(n) = 3*a(n-1)-2*a(n-2) for n>4. - Colin Barker, Apr 12 2016

From Paul Curtz, Sep 23 2019: (Start)

a(n+1) = b(n+4) - b(n) where b(n) = 0, 1, 1, 1 followed by A026646.

a(n) = 2*a(n-1)+4 for n>4. (End)

Prog

(Magma) [n le 2 select n else 5*2^(n-2)-4: n in [0..40]]; // Bruno Berselli, Apr 08 2016
(PARI) concat(0, Vec(x*(1-x+2*x^2+2*x^3)/((1-x)*(1-2*x)) + O(x^50))) \\ Colin Barker, Apr 12 2016

Crossrefs

Agrees with A048487 except for initial terms.

Cf. A002605, A265106, A265107, A265278.

Cf. A026646, A000225.

Sequence in context: A127902 A157136 A178523 * A366098 A227035 A257198

Adjacent sequences: A270807 A270808 A270809 * A270811 A270812 A270813

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 06 2016

Status

approved