A171473 a(n) = 6*a(n-1) - 8*a(n-2)-3 for n > 1; a(0) = 35, a(1) = 135.

35, 135, 527, 2079, 8255, 32895, 131327, 524799, 2098175, 8390655, 33558527, 134225919, 536887295, 2147516415, 8590000127, 34359869439, 137439215615, 549756338175, 2199024304127, 8796095119359, 35184376283135

Offset: 0

Author

Klaus Brockhaus, Dec 09 2009

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 22 in base 2: A061561(4*n+3) = 3*a(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A061561, A092431, A049775, A171470, A171471, A171472.

Programs

Magma

[32*4^n+4*2^n-1: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

PARI

{m=20; v=concat([35, 135], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

Formula

a(n) = 32*4^n + 4*2^n - 1.

G.f.: (35-110*x+72*x^2)/((1-x)*(1-2*x)*(1-4*x)).

a(n) = A092431(n+3).

a(n+1) - a(n) = A049775(n+5).

E.g.f.: exp(x)*(32*exp(3*x) + 4*exp(x) - 1). - Stefano Spezia, Sep 27 2023