login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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(n-1), 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 (list; graph; refs; listen; history; text; internal format)
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(n-1) 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 A276984

Adjacent sequences:  A094252 A094253 A094254 * A094256 A094257 A094258

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Apr 25 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 12:53 EST 2016. Contains 278738 sequences.