A254368 - OEIS

%I #16 Apr 26 2022 15:08:16

%S 21,28,44,82,176,418,1064,2842,7856,22258,64184,187402,551936,1635298,

%T 4864904,14512762,43374416,129795538,388731224,1164882922,3492027296,

%U 10470838978,31402031144,94185121882,282513422576,847456381618,2542201372664,7626268573642,22878134632256,68633061719458,205896500803784,617684133702202

%N a(n) = 5*2^n + 3^n + 15.

%C This is the sequence of third terms of "fifth partial sums of m-th powers".

%H Colin Barker, <a href="/A254368/b254368.txt">Table of n, a(n) for n = 0..1000</a>

%H Luciano Ancora, <a href="/A254368/a254368.pdf">Demonstration of formulas</a>, page 1.

%H Luciano Ancora, <a href="/A254368/a254368_1.pdf">Recurrence relations for partial sums of m-th powers</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

%F G.f.: -(107*x^2-98*x+21) / ((x-1)*(2*x-1)*(3*x-1)). - _Colin Barker_, Jan 30 2015

%F a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3). - _Colin Barker_, Jan 30 2015

%t Table[5 2^n + 3^n + 15, {n, 0, 30}] (* _Bruno Berselli_, Jan 30 2015 *)

%t LinearRecurrence[{6,-11,6},{21,28,44},40] (* _Harvey P. Dale_, Apr 26 2022 *)

%o (PARI) vector(30, n, n--; 5*2^n + 3^n + 15) \\ _Colin Barker_, Jan 30 2015

%Y Cf. A168614, A254369, A254370.

%K nonn,easy

%O 0,1

%A _Luciano Ancora_, Jan 29 2015