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A266507
a(n) = 6*a(n - 1) - a(n - 2) with a(0) = 2, a(1) = 8.
3
2, 8, 46, 268, 1562, 9104, 53062, 309268, 1802546, 10506008, 61233502, 356895004, 2080136522, 12123924128, 70663408246, 411856525348, 2400475743842, 13990997937704, 81545511882382, 475282073356588, 2770146928257146, 16145599496186288, 94103450048860582
OFFSET
0,1
COMMENTS
Bisection of A078343 = A078343(2*n + 1).
Quadrisection of A266504 = A266504(4*n + 1).
Octasection of A266506 = A266506(8*n + 2).
FORMULA
a(n) = (-sqrt(2)*(1+sqrt(2))^(2*n+1) - 3 *(1-sqrt(2))^(2*n+1) - sqrt(2)*(1-sqrt(2))^(2*n+1) + 3*(1+sqrt(2))^(2*n+1))/sqrt(8).
G.f.: 2*(1-2*x) / (1-6*x+x^2). - Colin Barker, Dec 31 2015
MATHEMATICA
LinearRecurrence[{6, -1}, {2, 8}, 70] (* Vincenzo Librandi, Dec 31 2015 *)
Table[SeriesCoefficient[2 (1 - 2 x)/(1 - 6 x + x^2), {x, 0, n}], {n, 0, 22}] (* Michael De Vlieger, Dec 31 2015 *)
PROG
(Magma) I:=[2, 8]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2): n in [1..70]]; // Vincenzo Librandi, Dec 31 2015
(PARI) Vec(2*(1-2*x)/(1-6*x+x^2) + O(x^30)) \\ Colin Barker, Dec 31 2015
CROSSREFS
Bisection of A078343 = A078343(2n + 1).
Quadrisection of A266504 = A266504(4n + 1).
Octasection of A266506 = A266506(8n + 2).
Equals 2*A038723(n).
Sequence in context: A119501 A183277 A269006 * A202081 A258315 A334498
KEYWORD
nonn,easy
AUTHOR
Raphie Frank, Dec 30 2015
STATUS
approved