A171477 a(n) = 6*a(n-1) - 8*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.

1, 7, 35, 155, 651, 2667, 10795, 43435, 174251, 698027, 2794155, 11180715, 44731051, 178940587, 715795115, 2863245995, 11453115051, 45812722347, 183251413675, 733006703275, 2932028910251, 11728119835307, 46912487729835

Offset: 0

Author

Klaus Brockhaus, Dec 09 2009

Keywords

• nonn
• easy

Comments

a(n) = A006095(n+2).

Second binomial transform of A168642.

Essentially partial sums of A006516.

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. A006095 (Gaussian binomial coefficient [n, 2] for q=2), A168642 ((8*2^n+(-1)^n)/3, a(0)=1), A006516 (2^(n-1)*(2^n-1)), A171472, A171473.

Programs

Magma

[(8*4^n-6*2^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

PARI

{m=23; v=concat([1, 7], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+1); v}

Formula

a(n) = (8*4^n-6*2^n+1)/3.

G.f.: 1/((1-x)*(1-2*x)*(1-4*x)).

a(n) = A139250(2^(n+1) - 1). - Omar E. Pol, Dec 20 2012