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A108354
Expansion of 1/((1-x)^2(1+x^2)^2) in powers of x.
0
1, 2, 1, 0, 2, 4, 2, 0, 3, 6, 3, 0, 4, 8, 4, 0, 5, 10, 5, 0, 6, 12, 6, 0, 7, 14, 7, 0, 8, 16, 8, 0, 9, 18, 9, 0, 10, 20, 10, 0, 11, 22, 11, 0, 12, 24, 12, 0, 13, 26, 13, 0, 14, 28, 14, 0, 15, 30, 15, 0, 16, 32, 16, 0, 17, 34, 17, 0, 18, 36, 18, 0, 19, 38, 19, 0, 20, 40, 20, 0, 21, 42, 21, 0, 22
OFFSET
0,2
COMMENTS
Self-convolution transform of A133872. - R. J. Mathar, Apr 06 2008
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
Cf. A133872.
Sequence in context: A174026 A226075 A279226 * A329099 A329686 A261615
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2005
STATUS
approved