|
|
A245581
|
|
a(n) = (5 * (1 + (-1)^(1 + n)) + 2 * n^2) / 4.
|
|
1
|
|
|
0, 3, 2, 7, 8, 15, 18, 27, 32, 43, 50, 63, 72, 87, 98, 115, 128, 147, 162, 183, 200, 223, 242, 267, 288, 315, 338, 367, 392, 423, 450, 483, 512, 547, 578, 615, 648, 687, 722, 763, 800, 843, 882, 927, 968, 1015, 1058, 1107, 1152, 1203, 1250, 1303, 1352, 1407
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = a(-n).
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). - Colin Barker, Jul 26 2014
G.f.: -x*(3*x^2-4*x+3) / ((x-1)^3*(x+1)). - Colin Barker, Jul 26 2014
E.g.f.: (exp(x)*x*(x+1) + 5*sinh(x))/2. - Peter Luschny, Aug 04 2014
|
|
MAPLE
|
|
|
MATHEMATICA
|
CoefficientList[Series[-x (3 x^2 - 4 x + 3)/((x - 1)^3 (x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 27 2014 *)
|
|
PROG
|
(Sage)
def A():
a, b, c, d = 0, 3, 2, 7
while True:
yield a
a, b, c, d = b, c, d, a + 2*(d - b)
(PARI) concat(0, Vec(-x*(3*x^2-4*x+3)/((x-1)^3*(x+1)) + O(x^100))) \\ Colin Barker, Jul 26 2014
(Magma) [(5*(1+(-1)^(1+n))+2*n^2) / 4: n in [0..60]]; // Vincenzo Librandi, Jul 27 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|