login
A164907
a(n) = (3*3^n-(-1)^n)/2.
3
1, 5, 13, 41, 121, 365, 1093, 3281, 9841, 29525, 88573, 265721, 797161, 2391485, 7174453, 21523361, 64570081, 193710245, 581130733, 1743392201, 5230176601, 15690529805, 47071589413, 141214768241, 423644304721, 1270932914165
OFFSET
0,2
COMMENTS
Interleaving of A096053 and A083884 without initial term 1.
Partial sums are (essentially) in A080926.
First differences are (essentially) in A105723.
a(n)+a(n+1) = A008776(n+1) = A099856(n+1) = A110593(n+2).
Binomial transform of A056450. Inverse binomial transform of A164908.
FORMULA
a(n) = 2*a(n-1)+3*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
G.f.: (1+3*x)/((1+x)*(1-3*x)).
a(n) = 3*a(n-1)+2*(-1)^n. - Carmine Suriano, Mar 21 2014
MAPLE
A164907:=n->(3*3^n - (-1)^n)/2; seq(A164907(n), n=0..30); # Wesley Ivan Hurt, Mar 21 2014
MATHEMATICA
Table[(3*3^n - (-1)^n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Mar 21 2014 *)
LinearRecurrence[{2, 3}, {1, 5}, 50] (* Harvey P. Dale, Oct 31 2018 *)
PROG
(Magma) [ (3*3^n-(-1)^n)/2: n in [0..25] ];
CROSSREFS
Equals A046717 without initial term 1 and A080925 without initial term 0. Equals A084182 / 2 from second term onward.
Sequence in context: A229747 A182300 A080925 * A046717 A352916 A085601
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Aug 31 2009
STATUS
approved