A254465 a(n) = 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56.
126, 252, 672, 2232, 8592, 36552, 166992, 804552, 4037712, 20923272, 111231312, 603667272, 3331889232, 18646768392, 105558814032, 603280840392, 3475274371152, 20152803339912, 117513698083152, 688425727971912, 4048693055291472, 23888489018765832, 141334996634766672, 838119509472869832
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Luciano Ancora, Demonstration of formulas, page 2.
- Luciano Ancora, Recurrence relations for partial sums of m-th powers
- Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
Programs
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Mathematica
Table[35 2^n + 10 4^n + 20 3^n + 4 5^n + 6^n + 56, {n, 0, 24}] (* Michael De Vlieger, Jan 31 2015 *) LinearRecurrence[{21,-175,735,-1624,1764,-720},{126,252,672,2232,8592,36552},30] (* Harvey P. Dale, Aug 02 2024 *) -
PARI
vector(30, n, n--; 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56) \\ Colin Barker, Jan 31 2015
Formula
G.f.: -6*(10036*x^5 -16454*x^4 +10065*x^3 -2905*x^2 +399*x -21) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)). - Colin Barker, Jan 31 2015
a(n) = 21*a(n-1)-175*a(n-2)+735*a(n-3)-1624*a(n-4)+1764*a(n-5)-720*a(n-6). - Colin Barker, Jan 31 2015
Comments