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URL: https://oeis.org/A220588

⇱ A220588 - OEIS

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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
OFFSET
0,3
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)
E.g.f.: exp(x)*(exp(x) - x*(2 + x)). - Stefano Spezia, Nov 21 2025
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
KEYWORD
sign,easy
AUTHOR
Dario Piazzalunga, Dec 16 2012
EXTENSIONS
a(3) corrected by Charles A. Dagino, Aug 16 2017
STATUS
approved