1,1

Four times the numerators of g.f. 1/(1-6x/5+x^2). - Ralf Stephan, Jun 12 2003

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.

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 430-433.

S. R. Finch, Plouffe's Constant

S. Plouffe, The Computation of Certain Numbers Using a Ruler and Compass, J. Integer Seqs. Vol. 1 (1998), #98.1.3.

A(n)=5^n sin(2n arctan(1/2)). A recursive formula for T(n) = tan(2n arctan(1/2)) is T(n+1)=(4/3+T(n))/(1-4/3*T(n)). Unsigned A(n) is the absolute value of numerator of T(n)

a(n) is the imaginary part of (2+I)^(2n) = sum(k=0, n, 2^(2*n-2*k-1)*(-1)^k*binomial(2*n, 2*k+1) ) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 03 2002

a[1] := 4/3; for n from 1 to 40 do a[n+1] := (4/3+a[n])/(1-4/3*a[n]):od: seq(abs(numer(a[n])), n=1..40); # a[n]=tan(2n arctan(1/2))

(PARI) a(n)=if(n<0, 0, imag((2+I)^(2*n))

Cf. A066771 5^n cos(2n arctan(1/2)), A000351 powers of 5 and also hypotenuse of right triangle with legs given by A066770 and A066771.

Note that A066770, A066771 and A0000351 are primitive Pythagorean triples with hypotenuse 5^n. The offset of A0000351 is zero, but the offset is 1 for A066770, A066771.

Adjacent sequences: A066767 A066768 A066769 this_sequence A066771 A066772 A066773

Sequence in context: A120622 A031117 A139245 this_sequence A080380 A039935 A090821

sign,easy,frac

Barbara Haas Margolius, (b.margolius(AT)csuohio.edu), Jan 17 2002