

A122514


Expansion of x/(1  2*x^2  x^3 + x^4).


0



0, 1, 0, 2, 1, 3, 4, 5, 10, 11, 21, 27, 43, 64, 92, 144, 205, 316, 462, 693, 1035, 1532, 2301, 3406, 5099, 7581, 11303, 16855, 25088, 37432, 55728, 83097, 123800, 184490, 274969, 409683, 610628, 909845, 1355970, 2020635, 3011157, 4487395, 6686979
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OFFSET

0,4


COMMENTS

a(n) is the number of compositions of n+2 such that: i) the first part is odd, ii) the last part is even, and iii) no two consecutive parts have the same parity.  Geoffrey Critzer, Mar 04 2012


LINKS

Table of n, a(n) for n=0..42.
Index entries for linear recurrences with constant coefficients, signature (0,2,1,1).


EXAMPLE

a(7) = 5 because there are 5 such compositions of the integer 9: 1+8, 7+2, 3+6, 5+4, 1+2+1+2+1+2.  Geoffrey Critzer, Mar 04 2012


MATHEMATICA

nn = 44; a = x/(1  x^2); b = x^2/(1  x^2); Drop[ CoefficientList[Series[1/(1  a b), {x, 0, nn}], x], 2] (* Geoffrey Critzer, Mar 04 2012 *)
CoefficientList[Series[x/(12x^2x^3+x^4), {x, 0, 50}], x] (* Harvey P. Dale, Jul 17 2019 *)


CROSSREFS

Cf. A006054, A006053.
Sequence in context: A308000 A029636 A293517 * A130077 A080412 A300948
Adjacent sequences: A122511 A122512 A122513 * A122515 A122516 A122517


KEYWORD

nonn,easy


AUTHOR

Roger L. Bagula, Sep 16 2006


STATUS

approved



