A171498 a(n) = 4*3^n-1.

3, 11, 35, 107, 323, 971, 2915, 8747, 26243, 78731, 236195, 708587, 2125763, 6377291, 19131875, 57395627, 172186883, 516560651, 1549681955, 4649045867, 13947137603, 41841412811, 125524238435, 376572715307, 1129718145923, 3389154437771, 10167463313315, 30502389939947

Offset: 0

Author

Klaus Brockhaus, Dec 10 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A171497.

Inverse binomial transform of A171499.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A010703, A036543, A171497, A171499.

Programs

Mathematica

NestList[3#+2&,3,30]  (* Harvey P. Dale, Feb 25 2011 *)

PARI

{m=25; v=concat([3], vector(m-1)); for(n=2, m, v[n]=3*v[n-1]+2); v}

Formula

a(n) = 3*a(n-1)+2 for n > 0; a(0) = 3.

G.f.: (3-x)/((1-x)*(1-3*x)).

a(n) = A036543(n) + 2. - Philippe Deléham, Apr 13 2013

E.g.f.: exp(x)*(4*exp(2*x) - 1). - Stefano Spezia, Aug 04 2024

Extensions

a(25)-a(27) from Stefano Spezia, Aug 04 2024