|
|
A136298
|
|
a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=9.
|
|
3
|
|
|
1, 2, 4, 9, 19, 41, 87, 185, 391, 825, 1735, 3641, 7623, 15929, 33223, 69177, 143815, 298553, 618951, 1281593, 2650567, 5475897, 11301319, 23301689, 48001479, 98799161, 203190727, 417566265, 857502151, 1759743545, 3608965575
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
O.g.f.: (1 -x -2*x^2 +x^3)/((1+x)*(1-2*x)^2).
a(n) = (7*2^n - (-1)^n)/9 + A001787(n+1)/12 if n>0. (End)
a(n) = (2^(n-2)*(3*n+31) - (-1)^n)/9 + (1/4)*[n=0].
E.g.f.: (1/36)*(9 - 4*exp(-x) + (31 + 6*x)*exp(2*x)). (End)
|
|
MATHEMATICA
|
LinearRecurrence[{3, 0, -4}, {1, 2, 4, 9}, 41] (* G. C. Greubel, Apr 12 2021 *)
|
|
PROG
|
(Magma) [1] cat [(2^(n-2)*(31+3*n) - (-1)^n)/9: n in [1..40]]; // G. C. Greubel, Apr 12 2021
(Sage) [1]+[(2^(n-2)*(31+3*n) - (-1)^n)/9 for n in (1..40)] # G. C. Greubel, Apr 12 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|