A024014 2^n-n^4.
1, 1, -12, -73, -240, -593, -1232, -2273, -3840, -6049, -8976, -12593, -16640, -20369, -22032, -17857, 0, 47551, 157168, 393967, 888576, 1902671, 3960048, 8108767, 16445440, 33163807, 66651888, 133686287, 267820800, 536163631, 1072931824
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..240
- Index entries for linear recurrences with constant coefficients, signature (7,-20,30,-25,11,-2).
Crossrefs
Programs
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Magma
[2^n-n^4: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011
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Magma
I:=[1,1,-12,-73,-240,-593]; [n le 6 select I[n] else 7*Self(n-1)-20*Self(n-2)+30*Self(n-3)-25*Self(n-4)+11*Self(n-5)-2*Self(n-6): n in [1..35]]; // Vincenzo Librandi, Oct 06 2014
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Maple
seq(2^n-n^4, n=0..100); # Robert Israel, Oct 06 2014
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Mathematica
Table[2^n-n^4,{n,0,100}] CoefficientList[Series[(1 - 6 x + x^2 + x^3 + 26 x^4 + x^5)/((1 - 2 x) (1 - x)^5), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
Formula
G.f.: (1-6*x+x^2+x^3+26*x^4+x^5) / ((1-2*x)*(1-x)^5). - Vincenzo Librandi, Oct 06 2014
a(n) = 7*a(n-1) -20*a(n-2) +30*a(n-3) -25*a(n-4) +11*a(n-5) -2*a(n-6) for n>5. - Vincenzo Librandi, Oct 06 2014
E.g.f.: exp(2*x) - (x + 7*x^2 + 6*x^3 + x^4)* exp(x). - Robert Israel, Oct 06 2014