A171479 a(n) = 6*a(n-1)-8*a(n-2)+3 for n > 1; a(0) = 1, a(1) = 8.
1, 8, 43, 197, 841, 3473, 14113, 56897, 228481, 915713, 3666433, 14672897, 58705921, 234852353, 939466753, 3757981697, 15032156161, 60129083393, 240517251073, 962070839297, 3848287027201, 15393155448833, 61572636475393
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8)
Programs
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Magma
[(2-7*2^n+7*4^n)/2: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011
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Maple
A171479:=n->(2-7*2^n+7*4^n)/2: seq(A171479(n), n=0..30); # Wesley Ivan Hurt, Apr 28 2017
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Mathematica
LinearRecurrence[{7,-14,8},{1,8,43},30] (* Harvey P. Dale, Sep 18 2022 *) -
PARI
{m=23; v=concat([1, 8], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+3); v}
Formula
a(n) = (2-7*2^n+7*4^n)/2.
G.f.: (1+x+x^2)/((1-x)*(1-2*x)*(1-4*x)).
E.g.f.: exp(x)*(2 - 7*exp(x) + 7*exp(3*x))/2. - Stefano Spezia, Feb 23 2025