|
|
A122514
|
|
Expansion of x/(1 - 2*x^2 - x^3 + x^4).
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|