OFFSET
1,2
COMMENTS
The 2 equations are equivalent to the Pell equation x^2- 285*y^2=1,
with x=(285*k+17)/2 and y=A*B/2, case C=15 in A160682.
Also: the first differences of A078366.
Positive values of x (or y) satisfying x^2 - 17xy + y^2 + 15 = 0. - Colin Barker, Feb 14 2014
LINKS
J.-C. Novelli and J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014-2020.
Index entries for linear recurrences with constant coefficients, signature (17,-1).
FORMULA
a(t+2) = 17*a(t+1)-a(t).
a(t) = ((285+15*w)*((17+w)/2)^(t-1)+(285-15*w)*((17-w)/2)^(t-1))/570, where w=sqrt(285).
a(t) = ceiling of ((285+15*w)*((17+w)/2)^(t-1))/570.
G.f.: x*(1-x)/(1-17*x+x^2).
a(n) = 17*a(n-1)-a(n-2). - Colin Barker, Feb 14 2014
MAPLE
t:=0: for a from 1 to 1000000 do b:=sqrt((19*a^2-4)/15):
if (trunc(b)=b) then t:=t+1: n:=(a^2-1)/15: print(t, a, b, n): end if: end do:
MATHEMATICA
Rest[CoefficientList[Series[x (1-x)/(1-17x+x^2), {x, 0, 40}], x]] (* or *) LinearRecurrence[{17, -1}, {1, 16}, 20] (* Harvey P. Dale, Oct 12 2012 *)
PROG
(PARI) Vec(x*(1-x)/(1-17*x+x^2) + O(x^100)) \\ Colin Barker, Feb 14 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Weisenhorn, Jun 14 2009
EXTENSIONS
Edited, extended by R. J. Mathar, Sep 02 2009
STATUS
approved