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%I #2 Mar 30 2012 17:25:05
%S 1,4,9,28,75,211,577,1591,4367,12004,32975,90607,248931,683946,
%T 1879112,5162835,14184754,38972316,107075529,294187633,808273837,
%U 2220714167,6101361970,16763354312,46056937364,126540395519
%N Let M = the 3 X 3 matrix [ 0 1 0 / 0 0 1 / -1, 3*sqrt(3), 3]. M^n * [1 1 1] = [ p q r]; then a(n-1), a(n), a(n+1) = floor p, q, r, respectively.
%C The matrix M is derived from a polynomial shown on p. 208 of "Advanced Trigonometry": sqrt(3)*x^3 - 3x^2 - 3*sqrt(3)*x + 1, which has roots tan 10 deg., tan 70 deg. and tan 130 deg. a(n)/a(n-1) tends to tan 70 deg. = 2.747477419...; e.g. a(11)/a(10) = 32975 / 12004 = 2.7470009...
%D C. V. Durell, A. Robson, "Advanced Trigonometry", Dover 2003, p. 208.
%e a(4), a(5), a(6) = 28, 75, 211 = floor: p, q, r; where M^5 * [1 1 1] = [p q r].
%K nonn
%O 1,2
%A _Gary W. Adamson_, Apr 25 2004
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