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A279269
a(n) = floor( (4 + sqrt(11))^n ).
1
1, 7, 53, 391, 2865, 20967, 153413, 1122471, 8212705, 60089287, 439650773, 3216759751, 23535824145, 172202794407, 1259943234533, 9218531904231, 67448539061185, 493495652968327, 3610722528440693, 26418301962683911, 193292803059267825, 1414250914660723047
OFFSET
0,2
COMMENTS
All numbers are odd.
FORMULA
O.g.f.: (1 - 2*x + 3*x^2)/((1 - x)*(1 - 8*x + 5*x^2)). - Ilya Gutkovskiy, Dec 13 2016
E.g.f.: exp((4 + sqrt(11))*x) + exp((4 - sqrt(11))*x) - exp(x). - Bruno Berselli, Dec 14 2016
a(n) = 9*a(n-1) - 13*a(n-2) + 5*a(n-3) for n>2.
a(n) = 8*a(n-1) - 5*a(n-2) + 2 for n>1.
a(n) = (4 + sqrt(11))^n + (4 - sqrt(11))^n - 1. - Bruno Berselli, Dec 13 2016
MATHEMATICA
Floor[(4+Sqrt[11])^Range[0, 30]] (* or *) LinearRecurrence[{9, -13, 5}, {1, 7, 53}, 30] (* Harvey P. Dale, Apr 22 2019 *)
CROSSREFS
Sequence in context: A223778 A223712 A065542 * A015561 A133588 A163306
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Dec 13 2016
STATUS
approved