|
|
A174029
|
|
a(n) = 3*(3*n+1)*(5 - (-1)^n)/4.
|
|
1
|
|
|
3, 18, 21, 45, 39, 72, 57, 99, 75, 126, 93, 153, 111, 180, 129, 207, 147, 234, 165, 261, 183, 288, 201, 315, 219, 342, 237, 369, 255, 396, 273, 423, 291, 450, 309, 477, 327, 504, 345, 531, 363, 558, 381, 585, 399, 612, 417, 639, 435, 666, 453
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
All entries are multiples of 3.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: ( 3 + 18*x + 15*x^2 + 9*x^3 ) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Jul 02 2011
a(n) = 2*a(n-2) - a(n-4); a(0)=3, a(1)=18, a(2)=21, a(3)=45. - Harvey P. Dale, Mar 19 2015
E.g.f.: (3/4)*(5*(1+3*x)*exp(x) - (1-3*x)*exp(-x)). - G. C. Greubel, Nov 02 2018
|
|
MATHEMATICA
|
LinearRecurrence[{0, 2, 0, -1}, {3, 18, 21, 45}, 60] (* Harvey P. Dale, Mar 19 2015 *)
|
|
PROG
|
(PARI) vector(50, n, n--; 3*(3*n+1)*(5-(-1)^n)/4) \\ G. C. Greubel, Nov 02 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|