

A094255


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(n1), a(n), a(n+1) = floor p, q, r, respectively.


0



1, 4, 9, 28, 75, 211, 577, 1591, 4367, 12004, 32975, 90607, 248931, 683946, 1879112, 5162835, 14184754, 38972316, 107075529, 294187633, 808273837, 2220714167, 6101361970, 16763354312, 46056937364, 126540395519
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OFFSET

1,2


COMMENTS

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(n1) tends to tan 70 deg. = 2.747477419...; e.g. a(11)/a(10) = 32975 / 12004 = 2.7470009...


REFERENCES

C. V. Durell, A. Robson, "Advanced Trigonometry", Dover 2003, p. 208.


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

a(4), a(5), a(6) = 28, 75, 211 = floor: p, q, r; where M^5 * [1 1 1] = [p q r].


CROSSREFS

Sequence in context: A120333 A000368 A232765 * A192234 A069563 A210969
Adjacent sequences: A094252 A094253 A094254 * A094256 A094257 A094258


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Apr 25 2004


STATUS

approved



