OFFSET
1,2
COMMENTS
This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:
A * c(n)+1 = a(n)^2,
(A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.
this is the b(n) sequence for A=7.
LINKS
Robert Israel, Table of n, a(n) for n = 1..610
Index entries for linear recurrences with constant coefficients, signature (30,-1).
FORMULA
G.f.: x*(1+x)/(x^2-30*x+1).
a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2) for n>2.
a(n) = ((15-4*sqrt(14))^(n-1)*(7-2*sqrt(14))+(7+2*sqrt(14))*(15+4*sqrt(14))^(n-1))/14. - Gerry Martens, Jul 09 2015
MAPLE
f:= gfun:-rectoproc({a(1) = 1, a(2) = 31, a(n) = 30*a(n-1)-a(n-2)}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 09 2015
MATHEMATICA
CoefficientList[Series[x*(1 + x)/(x^2 - 30 x + 1), {x, 0, 17}], x] (* Michael De Vlieger, Jul 09 2015 *)
LinearRecurrence[{30, -1}, {1, 31}, 20] (* Harvey P. Dale, Sep 05 2021 *)
PROG
(PARI) Vec((1+x)/(x^2-30*x+1)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Weisenhorn, Mar 08 2009
EXTENSIONS
Edited by Alois P. Heinz, Sep 09 2011
STATUS
approved