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A022406
a(0)=3, a(1)=7; thereafter a(n) = a(n-1) + a(n-2) + 1.
3
3, 7, 11, 19, 31, 51, 83, 135, 219, 355, 575, 931, 1507, 2439, 3947, 6387, 10335, 16723, 27059, 43783, 70843, 114627, 185471, 300099, 485571, 785671, 1271243, 2056915, 3328159, 5385075, 8713235, 14098311, 22811547, 36909859, 59721407, 96631267, 156352675
OFFSET
0,1
COMMENTS
a(n) is the minimum number of nodes required for a full binary AVL tree of height n+1 whose root node has a balance factor of 0. - Sumukh Patel, Jun 24 2022
FORMULA
a(n) = 4*A000045(n+2) - 1. - Ron Knott, Aug 25 2006
From R. J. Mathar, May 28 2008: (Start)
a(n) = A022403(n+1).
O.g.f.: (3+x-3*x^2)/((1-x)*(1-x-x^2)).
a(n+1) - a(n) = A022087(n+1).
(End)
a(n) = (2^(-n)*(-5*2^n + (10-6*sqrt(5))*(1-sqrt(5))^n + 2*(1+sqrt(5))^n*(5+3*sqrt(5)))) / 5. - Colin Barker, Mar 02 2018
MATHEMATICA
Table[4*Fibonacci[n + 2] - 1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)
CoefficientList[Series[(3+x-3*x^2)/((1-x)*(1-x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Mar 01 2018 *)
PROG
(PARI) for(n=0, 40, print1(4*fibonacci(n+2) -1, ", ")) \\ G. C. Greubel, Mar 01 2018
(Magma) [4*Fibonacci(n+2) - 1: n i [0..40]]; // G. C. Greubel, Mar 01 2018
CROSSREFS
Cf. A000045, A022087, A122195. See A022403 for a very similar sequence.
Sequence in context: A161387 A229086 A354902 * A355288 A132447 A132449
KEYWORD
nonn,easy
STATUS
approved