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 A171476 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1, a(0)=1, a(1)=6. 6
 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 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) = A006516(n+1). 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 a(n) = A020522(n+1)/2. - Hussam al-Homsi, Jun 06 2021 MATHEMATICA LinearRecurrence[{6, -8}, {1, 6}, 30] (* Harvey P. Dale, Aug 02 2020 *) 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)), A020522 (4^n-2^n), 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: A334410 A065997 A006516 * A171496 A330532 A037131 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 July 24 17:43 EDT 2021. Contains 346273 sequences. (Running on oeis4.)