

A134172


Expansion of x^2*(1+x)*(1x+x^2) / ((1x)^2*(1+x^2)^2).


2



0, 0, 1, 2, 1, 1, 4, 5, 2, 2, 7, 8, 3, 3, 10, 11, 4, 4, 13, 14, 5, 5, 16, 17, 6, 6, 19, 20, 7, 7, 22, 23, 8, 8, 25, 26, 9, 9, 28, 29, 10, 10, 31, 32, 11, 11, 34, 35, 12, 12, 37, 38, 13, 13, 40, 41, 14, 14, 43, 44, 15, 15, 46, 47, 16, 16, 49, 50, 17, 17, 52, 53, 18, 18, 55, 56, 19, 19, 58
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OFFSET

0,4


COMMENTS

Old definition was: "Starting with 0, 1, 2, 3, ... (A001477), write 0, 0 instead of a(0), 1, 1 instead of a(3) and in general n, n instead of a(3n)".


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,3,4,3,2,1).


FORMULA

From Colin Barker, May 30 2016: (Start)
G.f.: x^2*(1+x)*(1x+x^2) / ((1x)^2*(1+x^2)^2).
a(n) = (2+(i)^n+i^n+(4(1+i)*(i)^n(1i)*i^n)*n)/8 where i = sqrt(1).
a(n) = 2*a(n1)3*a(n2)+4*a(n3)3*a(n4)+2*a(n5)a(n6) for n>5. (End)


MATHEMATICA

LinearRecurrence[{2, 3, 4, 3, 2, 1}, {0, 0, 1, 2, 1, 1}, 50] (* G. C. Greubel, May 29 2016 *)


PROG

(PARI) concat(vector(2), Vec(x^2*(1+x)*(1x+x^2)/((1x)^2*(1+x^2)^2) + O(x^50))) \\ Colin Barker, May 30 2016


CROSSREFS

Sequence in context: A118686 A102610 A203300 * A208061 A078047 A329689
Adjacent sequences: A134169 A134170 A134171 * A134173 A134174 A134175


KEYWORD

nonn,easy


AUTHOR

Paul Curtz, Jan 13 2008


EXTENSIONS

New name using the g.f. from Colin Barker, May 30 2016


STATUS

approved



