OFFSET
0,2
COMMENTS
Also 13^n sin(2n arctan(2/3)) or numerator of tan(2n arctan(2/3)).
Note that a(n), A067359(n) and 13^n are primitive Pythagorean triples with hypotenuse 13^n.
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 430-433.
LINKS
J. M. Borwein and R. Girgensohn, Addition theorems and binary expansions, Canadian J. Math. 47 (1995) 262-273.
E. Eckert, The group of primitive Pythagorean triangles, Mathematics Magazine 57 (1984) 22-27.
Steven R. Finch, Plouffe's Constant [Broken link]
Steven R. Finch, Plouffe's Constant [From the Wayback machine]
Simon Plouffe, The Computation of Certain Numbers Using a Ruler and Compass, J. Integer Seqs. Vol. 1 (1998), #98.1.3.
Index entries for linear recurrences with constant coefficients, signature (10,-169).
FORMULA
G.f.: 12*x/(1-10*x+169*x^2). a(n)=10*a(n-1)-169*a(n-2). - Michael Somos, Jun 27 2002
MAPLE
a[1] := 12/5; for n from 1 to 40 do a[n+1] := (12/5+a[n])/(1-12/5*a[n]):od: seq(abs(numer(a[n])), n=1..40); # a[n]=tan(2n arctan(2/3))
MATHEMATICA
Im[(5 + 12*I)^Range[0, 24]] (* or *)
LinearRecurrence[{10, -169}, {0, 12}, 25] (* Paolo Xausa, Apr 22 2024 *)
PROG
(PARI) a(n)=imag((5+12*I)^n)
CROSSREFS
KEYWORD
sign,easy,frac
AUTHOR
Barbara Haas Margolius, (b.margolius(AT)csuohio.edu), Jan 17 2002
EXTENSIONS
Better description from Michael Somos, Jun 27 2002
STATUS
approved