A051794 a(n) = Sum_{i=n-6..n-1} (-1)^i * a(i), a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=1.

1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, 1, 1, 1, 2, -1, -3, 1, 1, 1, 1, 2, 5, -3, -7, 1, 1, 1, 0, 5, 13, -7, -15, 1, 1, 0, -5, 13, 33, -15, -31, 1, 2, -5, -23, 33, 81, -31, -63, 2, 9, -23, -79, 81, 193, -63, -128, 9, 41, -79, -239, 193, 449, -128, -265, 41, 161, -239

Offset

1,21

Comments

Same as the 12th-order equation given in the Mathematica program. - T. D. Noe, Feb 22 2012

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1,0,-1,0,1,0,1,0,1).

Formula

G.f.: -x*(x^2-x+1)*(x^2+x+1)*(2*x^7+x^6+x^5+x^4+x^3+x^2+x+1) / (x^12+x^10+x^8-x^6-x^4-x^2-1). - Colin Barker, Mar 17 2015

Mathematica

LinearRecurrence[{0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1}, {1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1}, 100] (* T. D. Noe, Feb 22 2012 *)

Prog

(PARI) Vec(-x*(x^2-x+1)*(x^2+x+1)*(2*x^7+x^6+x^5+x^4+x^3+x^2+x+1) / (x^12+x^10+x^8-x^6-x^4-x^2-1) + O(x^100)) \\ Colin Barker, Mar 17 2015

Crossrefs

Sequence in context: A125168 A324725 A328392 * A333305 A110969 A362681

Adjacent sequences: A051791 A051792 A051793 * A051795 A051796 A051797

Keyword

easy,nice,sign

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 10 1999

Status

approved