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A171476 a(n) = 6*a(n-1)-8*a(n-2) for n>1, a(0)=1, a(1)=6. 4
1, 6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776, 2096128, 8386560, 33550336, 134209536, 536854528, 2147450880, 8589869056, 34359607296, 137438691328, 549755289600, 2199022206976, 8796090925056, 35184367894528 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A006516(n+1).

Binomial transform of A048473; second binomial transform of A151821; third binomial transform of A010684; fourth binomial transform of A084633 without second term 0; fifth binomial transform of A168589.

Inverse binomial transform of A081625; second inverse binomial transform of A081626; third inverse binomial transform of A081627.

Partial sums of A010036.

Essentially first differences of A006095.

a(n) = A109241(n) converted from binary to decimal. - Robert Price, Jan 19 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Gordon Hamilton, Cookie Monster Counts Cookies (2010)

Index entries for linear recurrences with constant coefficients, signature (6,-8).

FORMULA

a(n) = sum( k=1..2^n-1, k ).

a(n) = 2*4^n-2^n.

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

a(n) = 4*a(n-1)+2^n for n>0, a(0)=1. [Vincenzo Librandi, Jul 17 2011]

a(n) = sum( k=0..n, 2^(n+k) ). [Bruno Berselli, Aug 07 2013]

PROG

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

(MAGMA) [2*4^n-2^n: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011

CROSSREFS

Cf. A006516 (2^(n-1)*(2^n-1)), A048473 (2*3^n-1), A151821 (powers of 2, omitting 2 itself), A010684 (repeat 1, 3), A084633 (inverse binomial transform of repeated odd numbers), A168589 ((2-3^n)*(-1)^n), A081625 (2*5^n-3^n), A081626 (2*6^n-4^n), A081627 (2*7^n-5^n), A010036 (sum of 2^n, ..., 2^(n+1)-1), A006095 (Gaussian binomial coefficient [n, 2] for q=2), A171472, A171473.

Sequence in context: A260508 A065997 A006516 * A171496 A037131 A292485

Adjacent sequences:  A171473 A171474 A171475 * A171477 A171478 A171479

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Dec 09 2009

STATUS

approved

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)