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 A176691 a(n) = 2^n + 2*n + 1. 11
 2, 5, 9, 15, 25, 43, 77, 143, 273, 531, 1045, 2071, 4121, 8219, 16413, 32799, 65569, 131107, 262181, 524327, 1048617, 2097195, 4194349, 8388655, 16777265, 33554483, 67108917, 134217783, 268435513, 536870971, 1073741885, 2147483711 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The subsequence of primes in this sequence is A163115. Also the number of connected dominating sets in the (n+1)-wheel graph. - Eric W. Weisstein, Aug 30 2017 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..3000 Eric Weisstein's World of Mathematics, Connected Dominating Set Eric Weisstein's World of Mathematics, Wheel Graph Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA a(n) = 2^n + 2*n + 1 = A000079(n) + A005843(n) + 1 = A000051(n) + A005843(n). From R. J. Mathar, Apr 28 2010: (Start) a(n) = +4*a(n-1) -5*a(n-2) +2*a(n-3). G.f.: ( -2+3*x+x^2 ) / ( (2*x-1)*(x-1)^2 ). (End) MAPLE seq(2^n+2*n+1, n=0..35); # Muniru A Asiru, Mar 25 2018 MATHEMATICA Table[2^n + 2 n + 1, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *) LinearRecurrence[{4, -5, 2}, {2, 5, 9}, 40] (* Vincenzo Librandi, Aug 12 2015 *) CoefficientList[Series[(-2 + 3 x + x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 30 2017 *) PROG (PARI) vector(40, n, n--; 2^n + 2*n + 1) \\ Michel Marcus, Aug 12 2015 (MAGMA) [2^n + 2*n + 1: n in [0..40]]; // Vincenzo Librandi, Aug 12 2015 (GAP) List([0..35], n->2^n+2*n+1); # Muniru A Asiru, Mar 25 2018 CROSSREFS Cf. A000051, A005126, A194455, A000079, A000290, A005843. Sequence in context: A100287 A007176 A267757 * A339554 A274355 A351100 Adjacent sequences:  A176688 A176689 A176690 * A176692 A176693 A176694 KEYWORD nonn,easy AUTHOR Jonathan Vos Post, Apr 23 2010 EXTENSIONS Corrected (one 1048617 replaced by 2097195) by R. J. Mathar, Apr 28 2010 STATUS approved

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Last modified June 28 01:48 EDT 2022. Contains 354903 sequences. (Running on oeis4.)