|
|
A135160
|
|
a(n) = 5^n + 3^n - 2^n.
|
|
9
|
|
|
1, 6, 30, 144, 690, 3336, 16290, 80184, 396930, 1972296, 9823650, 49003224, 244667970, 1222289256, 6108282210, 30531894264, 152630871810, 763068462216, 3815084423970, 19074648065304, 95370917376450, 476847616459176, 2384217167880930, 11921023089868344, 59604927188149890, 298024071132008136
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 5^n + 3^n - 2^n.
G.f.: 1/(1-5*x) + 1/(1-3*x) - 1/(1-2*x).
E.g.f.: e^(5*x) + e^(3*x) - e^(2*x). (End)
a(0)=1, a(1)=6, a(2)=30, a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - Harvey P. Dale, Mar 10 2013
|
|
EXAMPLE
|
a(4)=690 because 5^4=625, 3^4=81, 2^4=16 and we can write 625 + 81 - 16 = 690.
|
|
MATHEMATICA
|
Table[5^n+3^n-2^n, {n, 0, 30}] (* or *) LinearRecurrence[{10, -31, 30}, {1, 6, 30}, 30] (* Harvey P. Dale, Mar 10 2013 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|