A186948 a(n) = 3^n - 2*n.

1, 1, 5, 21, 73, 233, 717, 2173, 6545, 19665, 59029, 177125, 531417, 1594297, 4782941, 14348877, 43046689, 129140129, 387420453, 1162261429, 3486784361, 10460353161, 31381059565, 94143178781, 282429536433, 847288609393, 2541865828277, 7625597484933, 22876792454905, 68630377364825

Offset: 0

Author

Paul Barry, Mar 01 2011

Keywords

• nonn
• easy

Comments

Binomial transform is A186947 and A186949.

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A186947, A186949.

Programs

Mathematica

Table[3^n-2n,{n,0,30}] (* or *) LinearRecurrence[{5,-7,3},{1,1,5},30] (* Harvey P. Dale, Nov 24 2011 *)

PARI

a(n)=3^n-2*n \\ Charles R Greathouse IV, Oct 16 2015

Formula

G.f.: (1 - 4*x + 7*x^2)/((1-x)^2*(1-3*x)).

a(n) = 3*a(n-1) + 2*(2*n - 3). - Vincenzo Librandi, Mar 13 2011

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3); a(0)=1, a(1)=1, a(2)=5. - Harvey P. Dale, Nov 24 2011

E.g.f.: exp(x)*(exp(2*x) - 2*x). - Elmo R. Oliveira, Sep 15 2024

Extensions

a(26)-a(29) from Elmo R. Oliveira, Sep 15 2024