1,2

a(n)*(-1)^(n+1) is is the r=-3 member of the r-family of sequences S_r(n), n>=1, defined in A092184 where more information can be found.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

J. C. G. Nottrot, Vierkantenkransen rond een driehoek, Pythagoras (Netherlands), 14 (1975-1976) 77-81.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for sequences related to Chebyshev polynomials.

GF=x*(1-x)/(x^3-4*x^2-4*x+1), a(n)=4*(a(n-1)+a(n-2))-a(n-3), a(1)=1, a(2)=3, a(3)=16

a(n)=(2/7)*(T(n, 5/2)-(-1)^n) with twice Chebyshev's polynomials of the first kind evaluated at x=5/2: 2*T(n, 5/2)=A003501(n)= ((5+sqrt(21))^n + (5-sqrt(21))^n)/2^n. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

A005386:=-(-1+z)/(z+1)/(z**2-5*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

a[n_]:=Module[{n1=1, n2=0}, Do[{n1, n2}={Sqrt[3]*n1+n2, n1}, {n-1}]; n1^2] a[n_]:=Round[((5+Sqrt[21])/2)^n/7] (CoefficientList[Series[{(x/(1-x*(Sqrt[3]+x)))}, {x, 0, 20}], x])^2 CoefficientList[Series[{x*(1-x)/(x^3-4*x^2-4*x+1)}, {x, 0, 20}], x]

Essentially the same as A003769. First differences of A099025.

Sequence in context: A004303 A005947 A003769 this_sequence A053572 A055842 A037773

Adjacent sequences: A005383 A005384 A005385 this_sequence A005387 A005388 A005389

nonn

Jean Meeus

Edited by Peter J. C. Moses (mows(AT)mopar.freeserve.co.uk), Apr 23 2004

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 09 2004