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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A001580 a(n) = 2^n + n^2. 28 1, 3, 8, 17, 32, 57, 100, 177, 320, 593, 1124, 2169, 4240, 8361, 16580, 32993, 65792, 131361, 262468, 524649, 1048976, 2097593, 4194788, 8389137, 16777792, 33555057, 67109540, 134218457, 268436240 (list; graph; refs; listen; history; text; internal format) OFFSET 0,2 REFERENCES G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255. P. R. Halmos, Problems for Mathematicians Young and Old. Math. Assoc. America, 1991, p. 179. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA G.f.: (2*x-2*x^2+3*x^3-1)/(1-x)^3/(-1+2*x). a(n) = 2*A000217(n+1)+A000079(n) -3*A000027(n+1)+1. - R. J. Mathar, Nov 16 2007 MATHEMATICA f[n_]:=n^2+2^n; Table[f[n], {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 05 2009 *) LinearRecurrence[{5, -9, 7, -2}, {1, 3, 8, 17}, 30] (* Harvey P. Dale, Jan 05 2020 *) PROG (Magma) [2^n+n^2: n in [0..35]]; // Vincenzo Librandi, Jun 07 2011 (PARI) a(n)=2^n+n^2 \\ Charles R Greathouse IV, Apr 17 2012 (Maxima) A001580(n):=2^n+n^2$ makelist(A001580(n), n, 0, 20); /* Martin Ettl, Dec 18 2012 */ (Python) def A001580(n): return (1<<n)+n**2 # Chai Wah Wu, Apr 23 2023 CROSSREFS Sequence in context: A076980 A293057 A294417 * A360848 A002625 A027181 Adjacent sequences: A001577 A001578 A001579 * A001581 A001582 A001583 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified April 24 06:07 EDT 2024. Contains 371918 sequences. (Running on oeis4.)