|
|
A084174
|
|
a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4).
|
|
5
|
|
|
1, 1, 3, 6, 14, 29, 61, 124, 252, 507, 1019, 2042, 4090, 8185, 16377, 32760, 65528, 131063, 262135, 524278, 1048566, 2097141, 4194293, 8388596, 16777204, 33554419, 67108851, 134217714, 268435442, 536870897, 1073741809, 2147483632
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Original name was: Generalized Jacobsthal numbers.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^n + (-1)^n/4 - (2*n+1)/4.
a(n+2) = a(n+1) + 2*a(n) + n, a(0)=1, a(1)=1.
G.f.: (1 - 2*x + x^2 + x^3)/(1 - 3*x + x^2 + 3*x^3 - 2*x^4). - Colin Barker, Jan 16 2012
|
|
MAPLE
|
|
|
MATHEMATICA
|
LinearRecurrence[{3, -1, -3, 2}, {1, 1, 3, 6}, 40] (* Harvey P. Dale, Feb 17 2021 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|