OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,6,-8).
FORMULA
G.f.: (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)).
0 = 8*a(n) - 6*a(n+1) - 3*a(n+2) + a(n+3) for all n in Z.
E.g.f.: (exp(x) + exp(4*x) + exp(-2*x))/3. - G. C. Greubel, Sep 21 2019
EXAMPLE
G.f. = 1 + x + 7*x^2 + 19*x^3 + 91*x^4 + 331*x^5 + 1387*x^6 + 5419*x^7 + ...
MAPLE
seq((1 +(-2)^n +4^n)/3, n=0..30); # G. C. Greubel, Sep 21 2019
MATHEMATICA
CoefficientList[Series[(1-2x-2x^2)/((1-x)(1+2x)(1-4x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 25 2014 *)
LinearRecurrence[{3, 6, -8}, {1, 1, 7}, 30] (* Harvey P. Dale, Dec 04 2018 *)
PROG
(PARI) {a(n) = (1^n + (-2)^n + 4^n) / 3};
(PARI) {a(n) = if( n<0, 4^n, 1) * polcoeff( (1 - 2*x - 2*x^2) / ((1 - x) * (1 + 2*x) * (1 - 4*x)) + x * O(x^abs(n)), abs(n))};
(Magma) [(1^n + (-2)^n + 4^n) / 3 : n in [0..30]]; // Vincenzo Librandi, Jul 25 2014
(Sage) [(1 +(-2)^n +4^n)/3 for n in (0..30)] # G. C. Greubel, Sep 21 2019
(GAP) List([0..30], n-> (1 +(-2)^n +4^n)/3); # G. C. Greubel, Sep 21 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Jul 23 2014
STATUS
approved