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 A220588 a(n) = 2^n - n^2 - n. 1
 1, 0, -2, -4, -4, 2, 22, 72, 184, 422, 914, 1916, 3940, 8010, 16174, 32528, 65264, 130766, 261802, 523908, 1048156, 2096690, 4193798, 8388056, 16776616, 33553782, 67108162, 134216972, 268434644, 536870042, 1073740894, 2147482656, 4294966240, 8589933470, 17179867994 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2). FORMULA a(n) = 2*a(n - 1) + ((n - 3)^2 + 3(n - 3)) = 2*a(n - 1) + A028552(n - 3) for n > 4. a(n) = (2*a(n-1) + 7*a(n-2))*2 = A015519/2 for n > 4. From Colin Barker, Aug 16 2017: (Start) G.f.: (1 - 5*x + 7*x^2 - x^3) / ((1 - x)^3*(1 - 2*x)). a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>3. (End) EXAMPLE a(3) = -4 because 2^3 - 3^2 - 3 = 8 - 9 - 3 = -4. a(4) = -4 because 2^4 - 4^2 - 4 = 16 - 16 - 4 = -4. a(5) = 2 because 2^5 - 5^2 - 5 = 32 - 25 - 5 = 2. a(6) = 22 because 2^6 - 6^2 - 6 = 64 - 36 - 6 = 22. MATHEMATICA Table[2^n - n^2 - n, {n, 0, 32}] (* Alonso del Arte, Dec 16 2012 *) PROG (Maxima) A220588(n):=2^n-n^2-n\$ makelist(A220588(n), n, 0, 20); /* Martin Ettl, Dec 18 2012 */ (PARI) Vec((1 - 5*x + 7*x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Aug 16 2017 CROSSREFS Cf. A015519, A024012, A001580. Sequence in context: A193028 A203631 A188424 * A346262 A185356 A008777 Adjacent sequences: A220585 A220586 A220587 * A220589 A220590 A220591 KEYWORD sign,easy AUTHOR Dario Piazzalunga, Dec 16 2012 EXTENSIONS a(3) corrected by Charles A. Dagino, Aug 16 2017 STATUS approved

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Last modified June 4 03:42 EDT 2023. Contains 363118 sequences. (Running on oeis4.)