A122514 Expansion of x/(1 - 2*x^2 - x^3 + x^4).

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

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/(1-2x^2-x^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