0,3

a(n)*(-1)^(n+1) is the r=-4 member of the r-family of sequences S_r(n), n>=1, defined in A092184 where more information can be found.

T. Mansour, A note on sum of k-th power of Horadam's sequence

T. Mansour, Squaring the terms of an ell-th order linear recurrence

P. Stanica, Generating functions, weighted and non-weighted sums of powers...

Index entries for sequences related to Chebyshev polynomials.

G.f.: x*(1-x)/(1+x)/(1-6x+x^2). a(n)=(r^n+(1/r)^n-2*(-1)^n)/8, with r=3+sqrt(8). a(n+3)=5*a(n+2)+5*a(n+1)-a(n).

a(n+1) = sum_{k=0...n}((-1)^(n-k)*A001653(k)); e.g. 144 = -1 + 5 - 29 + 169; 25 = 1 - 5 + 29 - Charlie Marion (charliem(AT)bestweb.net), Jul 16 2003

a(n)=A000129(n)^2.

a(n)= (T(n, 3)-(-1)^n)/4 with Chebyshev's polynomials of the first kind evaluated at x=3: T(n, 3)=A001541(n)=((3+2*sqrt(2))^n + (3-2*sqrt(2))^n)/2. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

a(n) = rightmost term of M^n * [1 0 0] where M = the 3 X 3 matrix [4 4 1 / 2 1 0 / 1 0 0]. a(n+1) = leftmost term. E.g. a(6) = 4900, a(5) = 841 since M^5 * [1 0 0] = [4900 2030 841]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004

a(n) = [(-1)^(n+1)+A001109(n+1)-3*A001109(n)]/4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007

a(n) = ( ( ( (1-Sqrt[ 2 ])^n + (1+Sqrt[ 2 ])^n) /2 )^2 + (-1)^(n+1) ) /2 - Antonio Pane (apane1(AT)spc.edu), Dec 15 2007

with(combinat):seq(fibonacci(i, 2)^2, i=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008

Cf. A000129.

Cf. A001254, A007598.

Sequence in context: A123660 A156701 A015533 this_sequence A072221 A055846 A091634

Adjacent sequences: A079288 A079289 A079290 this_sequence A079292 A079293 A079294

easy,nonn

Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 08 2003