|
|
A027688
|
|
a(n) = n^2 + n + 3.
|
|
18
|
|
|
3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, 135, 159, 185, 213, 243, 275, 309, 345, 383, 423, 465, 509, 555, 603, 653, 705, 759, 815, 873, 933, 995, 1059, 1125, 1193, 1263, 1335, 1409, 1485, 1563, 1643, 1725, 1809, 1895, 1983, 2073, 2165, 2259
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (3*x^2 - 4*x + 3)/(1 - x)^3. (End)
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(11)/2)/sqrt(11). - Amiram Eldar, Jan 17 2021
|
|
MAPLE
|
with (combinat):seq(fibonacci(3, n)+n+2, n=0..47); # Zerinvary Lajos, Jun 07 2008
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) Vec((3*x^2-4*x+3)/(1-x)^3 + O(x^100)) \\ Colin Barker, Dec 29 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|