A024013 -id:A024013 - cp's OEIS frontend

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

N. J. A. Sloane

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).

Cf. A024012, A024013.

Cf. sequences of the form k^n-n^4: this sequence (k=2), A024027 (k=3), A024040 (k=4), A024053 (k=5), A024066 (k=6), A024079 (k=7), A024092 (k=8), A024105 (k=9), A024118 (k=10), A024131 (k=11), A024144 (k=12).

[2^n-n^4: n in [0..30]]; // Vincenzo Librandi, Apr 29 2011

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

seq(2^n-n^4, n=0..100); # Robert Israel, Oct 06 2014

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 *)

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

A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k.

Original entry on oeis.org

0, 5, 0, 7, 28, 79, 192, 431, 24, 717, 2368, 5995, 13640, 29393, 0, 47551, 157168, 393967, 888576, 1902671, 3960048, 1952265, 8814592, 23788807, 55227488, 119868821, 251225088, 516359763, 344741824, 1259979967, 3221225472, 7298466623, 15635064768

Offset: 2

Alex Ratushnyak, Aug 25 2012

nonn

			a(2) = 2^2 - 2^2 = 0,
a(3) = 2^3 - 3 = 5,
a(4) = 2^4 - 4^2 = 0,
a(5) = 2^5 - 5^2 = 7,
a(6)..a(9) are 2^n - n^2,
a(10)..a(15) are 2^n - n^3,
a(16)..a(22) are 2^n - n^4, and so on.

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Cf. A000325, A024012, A024013, A024014, A024015, A024016.
Cf. A024017, A024018, A024019, A024020, A024021, A024022.
Cf. A060508.

[2^n - n^Floor(n*Log(n, 2)): n in [2..40]]; // Vincenzo Librandi, Jan 14 2019

Table[2^n - n^Floor[n*Log[n, 2]], {n, 2, 35}] (* T. D. Noe, Aug 27 2012 *)

for n in range(2,100):
    a = 2**n
    k = 0
    while n**(k+1) <= a:
        k += 1
    print(a - n**k, end=',')

a(n) = 2^n - n^floor(n*log_n(2)), where log_n is the base-n logarithm.

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A024014 2^n-n^4.

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A215892 a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k.

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