OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (1st line of Table 1).
Index entries for linear recurrences with constant coefficients, signature (4,-4,1).
FORMULA
a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3), n >= 4.
From Colin Barker, Sep 17 2017: (Start)
G.f.: 3*x^2*(1 - 2*x) / ((1 - x)*(1 - 3*x + x^2)).
a(n) = 3*(1 + (2^(-1-n)*((7-3*sqrt(5))*(3+sqrt(5))^n - (3-sqrt(5))^n*(7+3*sqrt(5)))) / sqrt(5)) for n>0.
(End)
a(n) = 3*(Fibonacci(2*n - 4) + 1) for n > 0. - Ehren Metcalfe, Apr 18 2019
MATHEMATICA
CoefficientList[Series[3*x^2*(1 - 2*x)/((1 - x)*(1 - 3*x + x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)
PROG
(PARI) concat(vector(2), Vec(3*x^2*(1 - 2*x) / ((1 - x)*(1 - 3*x + x^2)) + O(x^30))) \\ Colin Barker, Sep 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Sep 13 2017
STATUS
approved