OFFSET
0,1
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7, -14, 8).
FORMULA
a(n) = 2*4^(n+5)+91*2^(n+2)-1 for n > 0.
G.f.: (775+3494*x-17360*x^2+13088*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
G.f. for the sequence starting at a(1): x*(8919-28210*x+19288*x^2) / ((1-x)*(1-2*x)*(1-4*x)).
a(0)=775, a(1)=8919, a(2)=34223, a(3)=133983, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - Harvey P. Dale, Mar 04 2013
MATHEMATICA
nxt[{a_, b_}]:={b, 6b-8a-3}; Join[{775}, Transpose[NestList[nxt, {8919, 34223}, 20]][[1]]] (* or *) Join[{775}, LinearRecurrence[{7, -14, 8}, {8919, 34223, 133983}, 20]] (* Harvey P. Dale, Mar 04 2013 *)
CoefficientList[Series[(775 + 3494 x - 17360 x^2 + 13088 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
PROG
(PARI) {m=19; v=concat([775, 8919, 34223], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}
(Magma) [775] cat [2*4^(n+5)+91*2^(n+2)-1: n in [1..25]]; // Vincenzo Librandi, Sep 24 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, May 14 2010
STATUS
approved