OFFSET
0,2
COMMENTS
Self-convolution transform of A133872. - R. J. Mathar, Apr 06 2008
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).
FORMULA
a(n)=2a(n-1)-3a(n-2)+4a(n-3)-3a(n-4)+2a(n-5)-a(n-6); a(n)=cos(pi*n/2)/4+(n+3)*sin(pi*n/2)/4+(n+3)/4.
Euler transform of length 4 sequence [ 2, -2, 0, 2]. - Michael Somos, Aug 17 2014
0 = a(n)*(+2*a(n+2) - a(n+3)) + a(n+1)*(-a(n+2) + 2*a(n+3)) for all n in Z. - Michael Somos, Aug 17 2014
EXAMPLE
G.f. = 1 + 2*x + x^2 + 2*x^4 + 4*x^5 + 2*x^6 + 3*x^8 + 6*x^9 + 3*x^10 + ...
MATHEMATICA
CoefficientList[Series[1/((1-x)^2 (1+x^2)^2), {x, 0, 100}], x] (* or *)
LinearRecurrence[{2, -3, 4, -3, 2, -1}, {1, 2, 1, 0, 2, 4}, 100](* Harvey P. Dale, Apr 11 2020 *)
PROG
(PARI) {a(n) = (n\4+1) * [1, 2, 1, 0][n%4+1]};
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2005
STATUS
approved