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A157456 Expansion of x * (1 - x) / (1 - 16*x + x^2). 21
1, 15, 239, 3809, 60705, 967471, 15418831, 245733825, 3916322369, 62415424079, 994730462895, 15853271982241, 252657621252961, 4026668668065135, 64174041067789199, 1022757988416562049, 16299953773597203585, 259776502389138695311, 4140124084452621921391 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Positive values of x (or y) satisfying x^2 - 16xy + y^2 + 14 = 0. - Colin Barker, Feb 11 2014
LINKS
J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014.
FORMULA
G.f.: x*(1-x) / ( 1-16*x+x^2 ). - R. J. Mathar, Oct 31 2011
a(n) = 16*a(n-1)-a(n-2). - Colin Barker, Feb 11 2014
a(n) = (1/18)*(9-sqrt(63))*(1+(8+sqrt(63))^(2*n-1))/(8+sqrt(63))^(n-1). [Bruno Berselli, Feb 25 2014]
a(n) = sqrt(2+(8-3*sqrt(7))^(1+2*n)+(8+3*sqrt(7))^(1+2*n))/(3*sqrt(2)). - Gerry Martens, Jun 06 2015
a(n) = A077412(n-1) - A077412(n-2). - R. J. Mathar, Feb 05 2020
MAPLE
f:= gfun:-rectoproc({a(n)=16*a(n-1)-a(n-2), a(1)=1, a(2)=15}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 07 2015
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - 16 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 12 2014 *)
LinearRecurrence[{16, -1}, {1, 15}, 20] (* Harvey P. Dale, Sep 17 2019 *)
PROG
(Magma) I:=[1, 15]; [n le 2 select I[n] else 16*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Feb 12 2014
CROSSREFS
Cf. A159678.
Cf. similar sequences listed in A238379.
Sequence in context: A209118 A093745 A071811 * A343527 A097262 A158557
KEYWORD
nonn,easy
AUTHOR
Paul Weisenhorn, Mar 01 2009
EXTENSIONS
New name (using the g.f. by R. J. Mathar) from Joerg Arndt, Jun 06 2015
STATUS
approved

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Last modified April 16 00:27 EDT 2024. Contains 371696 sequences. (Running on oeis4.)