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 A141025 a(n) = (2^(2+n)-(-1)^n)/3 - 2*n. 1
 1, 1, 1, 5, 13, 33, 73, 157, 325, 665, 1345, 2709, 5437, 10897, 21817, 43661, 87349, 174729, 349489, 699013, 1398061, 2796161, 5592361, 11184765, 22369573, 44739193, 89478433, 178956917, 357913885, 715827825, 1431655705, 2863311469, 5726622997, 11453246057, 22906492177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2). FORMULA a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4). a(n) = A001045(n+2) - 2*n. a(n+1) - a(n) = 4*A000975(n-1). a(n+1) - 2*a(n)= 2*(n-1) + (-1)^n = -1, -1, 3, 3, 7, 7, 11, 11,... duplicated A004767. G.f. ( -1+2*x+x^2-6*x^3 ) / ( (1+x)*(2*x-1)*(x-1)^2 ). - R. J. Mathar, Jul 07 2011 MATHEMATICA CoefficientList[Series[(-1 + 2*x + x^2 - 6*x^3)/((1 + x)*(2*x - 1)*(x - 1)^2), {x, 0, 50}], x] (* G. C. Greubel, Oct 11 2017 *) PROG (MAGMA) [(2^(2+n)-(-1)^n)/3-2*n: n in [0..40]]; // Vincenzo Librandi, Aug 08 2011 (PARI) for(n=0, 50, print1((2^(2+n)-(-1)^n)/3 - 2*n, ", ")) \\ G. C. Greubel, Oct 11 2017 CROSSREFS Sequence in context: A272161 A272828 A001981 * A100227 A185454 A278764 Adjacent sequences:  A141022 A141023 A141024 * A141026 A141027 A141028 KEYWORD nonn,easy AUTHOR Paul Curtz, Jul 29 2008 EXTENSIONS Definition replaced by closed form by R. J. Mathar, Jul 07 2011 STATUS approved

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Last modified February 19 09:34 EST 2018. Contains 299330 sequences. (Running on oeis4.)