|
|
A097063
|
|
Expansion of (1-2*x+3*x^2)/((1+x)*(1-x)^3).
|
|
8
|
|
|
1, 0, 3, 4, 9, 12, 19, 24, 33, 40, 51, 60, 73, 84, 99, 112, 129, 144, 163, 180, 201, 220, 243, 264, 289, 312, 339, 364, 393, 420, 451, 480, 513, 544, 579, 612, 649, 684, 723, 760, 801, 840, 883, 924, 969, 1012, 1059, 1104, 1153, 1200, 1251, 1300, 1353, 1404
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
G.f. : (1-2*x+3*x^2)/((1-x^2)(1-x)^2).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
a(n) = Sum_{k=0..n} (k^2-k+1)*(-1)^(n-k).
a(n) = binomial(n+1, 2) - ceiling((n+1)/2) + 2((n+1) mod 2). - Wesley Ivan Hurt, Mar 08 2014
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(1/4) + (3/4)*(-1)^n + (1/2)*n^2, {n, 0, 50}] (* Wesley Ivan Hurt, Mar 08 2014 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|