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 A171499 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 3, a(1) = 14. 8
 3, 14, 60, 248, 1008, 4064, 16320, 65408, 261888, 1048064, 4193280, 16775168, 67104768, 268427264, 1073725440, 4294934528, 17179803648, 68719345664, 274877644800, 1099511103488, 4398045462528, 17592183947264, 70368739983360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Binomial transform of A171498; second binomial transform of A171497; third binomial transform of A010703. Related to sequences A001969 and A000069, sum of each group with exponent 1. - Eric Desbiaux, Jul 24 2013 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (6,-8) FORMULA a(n) = 4*4^n - 2^n = 2^n * (2^(n+2)-1). G.f.: (3-4*x)/((1-2*x)*(1-4*x)). a(n) = 4*a(n-1)+2^n, a(0)=3; a(n) = 6*a(n-1) - 8*a(n-2). [Vincenzo Librandi, Jul 18 2011] MATHEMATICA (* This program shows how A171499 arises from the Vandermonde determinant of (1, 2, 4, ..., 2^(n-1)). *) f[j_] := 2^(j - 1); z = 15; v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}] d[n_] := Product[(i - 1)!, {i, 1, n}] Table[v[n], {n, 1, z}]               (* A203303 *) Table[v[n + 1]/v[n], {n, 1, z - 1}]  (* A002884 *) Table[v[n] v[n + 2]/(2*v[n + 1]^2),   {n, 1, z - 1}]                       (* A171499 *) (* Clark Kimberling, Jan 02 2011 *) PROG (PARI) {m=23; v=concat([3, 14], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v} (MAGMA) [4*4^n-2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011 CROSSREFS Cf. A010703, A171497, A171498, A171472, A171473. Sequence in context: A006224 A219544 A131262 * A006502 A024037 A281349 Adjacent sequences:  A171496 A171497 A171498 * A171500 A171501 A171502 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Dec 10 2009 STATUS approved

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Last modified October 23 07:11 EDT 2019. Contains 328336 sequences. (Running on oeis4.)