OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Moussa Benoumhani, On the Modes of the Independence Polynomial of the Centipede, Journal of Integer Sequences, Vol. 15 (2012), #12.5.1.
É. Czabarka, R. Flórez, and L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.
Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-4,1,1).
FORMULA
EXAMPLE
a(4)=5 because in 1110', 1111, 1101, 10'10', 10'11, 0110', 0111 and 0101 one has altogether five 0's in even position (marked by ').
MAPLE
G:=z^2/(1-z-z^2)^2/(1+z-z^2): Gser:=series(G, z=0, 45): seq(coeff(Gser, z, n), n=0..42);
MATHEMATICA
CoefficientList[Series[x^2/((1 + x - x^2)*(1 - x - x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Mar 09 2017 *)
LinearRecurrence[{1, 4, -3, -4, 1, 1}, {0, 0, 1, 1, 5, 6}, 40] (* Harvey P. Dale, Apr 02 2018 *)
PROG
(PARI) x='x+O('x^50); concat([0, 0], Vec(x^2/((1 + x - x^2)*(1 - x - x^2)^2))) \\ G. C. Greubel, Mar 09 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 13 2007
STATUS
approved