login
A135162
a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order.
1
0, 1, 19, 199, 1711, 13471, 101359, 743359, 5367871, 38381311, 272651599, 1928323519, 13596619231, 95666721151, 672114790639, 4717029615679, 33080299697791, 231867445524991, 1624598513486479, 11379820537307839, 79696895380235551, 558069016466824831, 3907436831415107119
OFFSET
0,3
FORMULA
a(n) = 7^n - 5^n - 3^n + 2^n.
a(0)=0, a(1)=1, a(2)=19, a(3)=199, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Dec 13 2013
G.f.: 1/(1-7*x) - 1/(1-5*x) - 1/(1-3*x) + 1/(1-2 x). - Vincenzo Librandi, May 22 2014
E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) + exp(2*x). - G. C. Greubel, Sep 30 2016
EXAMPLE
a(4) = 1711 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625-81+16 = 1711.
MATHEMATICA
Table[7^n-5^n-3^n+2^n, {n, 0, 30}] (* or *) LinearRecurrence[ {17, -101, 247, -210}, {0, 1, 19, 199}, 30] (* Harvey P. Dale, Dec 13 2013 *)
CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) - 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
PROG
(Magma) [7^n-5^n-3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
(PARI) a(n) = 7^n - 5^n - 3^n + 2^n \\ Charles R Greathouse IV, Sep 30 2016
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Nov 21 2007
EXTENSIONS
More terms from Vincenzo Librandi, Dec 14 2010
STATUS
approved