A024079 a(n) = 7^n - n^4.

1, 6, 33, 262, 2145, 16182, 116353, 821142, 5760705, 40347046, 282465249, 1977312102, 13841266465, 96888981846, 678223034433, 4747561459318, 33232930504065, 232630513903686, 1628413597805473, 11398895185242822

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (12,-45,80,-75,36,-7).

Programs

Magma

[7^n-n^4: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011

Mathematica

Array[7^# - #^4 &, 20, 0] (* or *)
CoefficientList[Series[(6 x^5 + 81 x^4 + 56 x^3 + 6 x^2 - 6 x + 1)/((x - 1)^5*(7 x - 1)), {x, 0, 19}], x] (* Michael De Vlieger, May 13 2017 *)
LinearRecurrence[{12,-45,80,-75,36,-7},{1,6,33,262,2145,16182},20] (* Harvey P. Dale, Feb 02 2020 *)

Formula

From Chai Wah Wu, May 13 2017: (Start)

a(n) = 12*a(n-1) - 45*a(n-2) + 80*a(n-3) - 75*a(n-4) + 36*a(n-5) - 7*a(n-6) for n > 5.

G.f.: (6*x^5 + 81*x^4 + 56*x^3 + 6*x^2 - 6*x + 1)/((x - 1)^5*(7*x - 1)). (End)