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 A101945 a(n) = 6*2^n - n - 5. 2
 1, 6, 17, 40, 87, 182, 373, 756, 1523, 3058, 6129, 12272, 24559, 49134, 98285, 196588, 393195, 786410, 1572841, 3145704, 6291431, 12582886, 25165797, 50331620, 100663267, 201326562, 402653153, 805306336, 1610612703, 3221225438 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Characteristic polynomial of M = x^3 - 4x^2 + 5x - 2. Recursive sequence generated from a 3 X 3 matrix. No exponentiation is needed! - Vladimir Joseph Stephan Orlovsky, Oct 10 2008 LINKS FORMULA a(0)=1, a(1)=6, a(2)=17 and for n>2, a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). a(n) = right term in M^n * [1 1 1]. M^n * [1 1 1] = [1 A033484(n) a(n)]. Row sums of triangle A135855. - Gary W. Adamson, Dec 01 2007 EXAMPLE a(5) = 182 = 4*87 - 5*40 + 2*17 = 4*a(4) - 5*a(3) + 2*a(2). a(5) = 182 = right term in M^5 * [1 1 1]; where M^5 * [ 1 1 1] = [1 94 182] = [1 A033484(5) a(5)]. MATHEMATICA a[0] = 1; a[1] = 6; a[2] = 17; a[n_] := a[n] = 4a[n - 1] - 5a[n - 2] + 2a[n - 3]; Table[ a[n], {n, 0, 30}] (* Robert G. Wilson v, Jan 12 2005 *) s=1; lst={}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 3, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 10 2008 *) PROG (PARI) a(n)=if(n==1, 1, if(n==2, 6, if(n==3, 17, 4*a(n-1)-5*a(n-2)+2*a(n-3)))) \\ (Klasen) CROSSREFS Cf. A033484, A101946. Cf. A135855. Sequence in context: A080275 A061349 A213780 * A220407 A013319 A047861 Adjacent sequences:  A101942 A101943 A101944 * A101946 A101947 A101948 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Dec 22 2004 EXTENSIONS More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 06 2005 New definition from Ralf Stephan, May 17 2007 STATUS approved

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Last modified June 25 04:06 EDT 2019. Contains 324345 sequences. (Running on oeis4.)