OFFSET
0,2
COMMENTS
Inverse binomial transform of 3^n, with 3 (second term) excluded.
a(n) mod 9 gives A010689.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2).
FORMULA
a(n) = a(n-1) + 2*a(n-2) for n>1, a(0)=1, a(1)=8.
a(n) = 2*a(n-1) - 6*(-1)^n for n>0, a(0)=1.
a(n+2) - a(n) = a(n) + a(n+1) = A005010(n).
G.f.: -(7*x+1) / ((x+1)*(2*x-1)). - Colin Barker, Jul 03 2015
MATHEMATICA
Table[3 2^n - 2 (-1)^n, {n, 0, 50}] (* Vincenzo Librandi, Jul 04 2015 *)
LinearRecurrence[{1, 2}, {1, 8}, 40] (* Harvey P. Dale, Aug 19 2020 *)
PROG
(PARI) Vec(-(7*x+1)/((x+1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Jul 03 2015
(Magma) [3*2^n-2*(-1)^n: n in [0..40]]; // Vincenzo Librandi, Jul 04 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Jul 03 2015
EXTENSIONS
Typo in data fixed by Colin Barker, Jul 03 2015
STATUS
approved