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A247035
Expansion of 2*(x+1)*(x^4+6*x^3+5*x^2+6*x+1)/(x^6-18*x^3+1).
1
2, 14, 22, 58, 266, 398, 1042, 4774, 7142, 18698, 85666, 128158, 335522, 1537214, 2299702, 6020698, 27584186, 41266478, 108037042, 494978134, 740496902, 1938646058, 8882022226, 13287677758, 34787592002, 159381421934, 238437702742, 624238009978
OFFSET
0,1
LINKS
FORMULA
G.f.: 2*(x+1)*(x^4+6*x^3+5*x^2+6*x+1)/(x^6-18*x^3+1).
a(n) = (7/2)*( 3*F(2n)+F(2n-1) ) if n==1 (mod 3); otherwise a(n) = 2*( 3*F(2n)+F(2n-1) ), where F = A000045. [Robert Israel, see Link section]
MATHEMATICA
CoefficientList[Series[2 (x + 1) (x^4 + 6 x^3 + 5 x^2 + 6 x + 1)/(x^6 - 18 x^3 + 1), {x, 0, 30}], x]
LinearRecurrence[{0, 0, 18, 0, 0, -1}, {2, 14, 22, 58, 266, 398}, 30] (* Harvey P. Dale, Jul 27 2018 *)
PROG
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients (R!(2*x*(x+1)*(x^4+6*x^3+5*x^2+6*x+1)/(x^6-18*x^3+1)));
(Magma) A002878:=func<i | 3*Fibonacci(2*i)+Fibonacci(2*i-1)>; [IsOne(n mod 3) select (7/2)*A002878(n) else 2*A002878(n): n in [0..30]]; // Bruno Berselli, Sep 10 2014
CROSSREFS
Sequence in context: A074312 A061426 A190045 * A069512 A328217 A116639
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Sep 10 2014
STATUS
approved