|
|
A275155
|
|
a(1) = 18; a(n) = 3*a(n - 1) + 2*sqrt(2*a(n - 1)*(a(n - 1) - 14)) - 14 for n > 1.
|
|
1
|
|
|
18, 64, 338, 1936, 11250, 65536, 381938, 2226064, 12974418, 75620416, 440748050, 2568867856, 14972459058, 87265886464, 508622859698, 2964471271696, 17278204770450, 100704757350976, 586950339335378, 3420997278661264, 19939033332632178, 116213202717131776
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
a(n+1) = 3*a(n) + 2*sqrt(2*a(n)*(a(n) - 14)) - 14.
a(n) = (14+(9-4*sqrt(2))*(3+2*sqrt(2))^n + (3-2*sqrt(2))^n*(9+4*sqrt(2)))/2.
a(n) = 7*a(n-1) -7*a(n-2) +a(n-3) for n>3.
G.f.: 2*x*(9-31*x+8*x^2) / ((1-x)*(1-6*x+x^2)). (End)
|
|
MATHEMATICA
|
CoefficientList[Series[2*x*(9-31*x+8*x^2)/((1-x)*(1-6*x+x^2)), {x, 0, 50}], x] (* G. C. Greubel, Sep 30 2018 *)
|
|
PROG
|
(PARI) Vec(2*x*(9-31*x+8*x^2)/((1-x)*(1-6*x+x^2)) + O(x^30)) \\ Colin Barker, Jul 21 2016
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*x*(9-31*x+8*x^2)/((1-x)*(1-6*x+x^2)))); // G. C. Greubel, Sep 30 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|