A195116 a(n) = (2+3^n)*(3+2^n).

12, 25, 77, 319, 1577, 8575, 48977, 286759, 1699817, 10137775, 60645377, 363332599, 2178384857, 13065493375, 78378545777, 470228096839, 2821239178697, 16927047127375, 101561119454177, 609363227843479, 3656168902513337, 21936982025631775

Offset: 0

Author

Bruno Berselli, Sep 09 2011

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).

Crossrefs

Cf. A060013 ((1+2^n)*(2+1) with n>3).

Cf. A021029 (for the recurrence).

Programs

Magma

[(2+3^n)*(3+2^n): n in [0..21]];

Mathematica

Table[(2 + 3^n) (3 + 2^n), {n, 0, 30}] (* Vincenzo Librandi, Mar 26 2013 *)

PARI

for(n=0, 21, print1((2+3^n)*(3+2^n)", "));

Python

def a(n): return (2+3**n)*(3+2**n)
print([a(n) for n in range(23)]) # Michael S. Branicky, Dec 25 2021

Formula

G.f.: (12-119*x+341*x^2-294*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).

Sum_{i=0..n} a(i) = (1/10)*(12*6^n+45*3^n+40*2^n+60*n+23).