A254369 - OEIS

%I #17 Dec 04 2020 19:28:08

%S 56,84,156,354,936,2754,8736,29274,102216,368274,1359216,5110794,

%T 19495896,75203394,292596096,1145977914,4511183976,17827536114,

%U 70660511376,280697078634,1116961278456,4450379734434,17749154257056,70839585900954,282887376051336,1130136853206354,4516309963145136,18052528510172874,72171982026734616

%N a(n) = 15*2^n + 4^n + 5*3^n + 35.

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

%H Colin Barker, <a href="/A254369/b254369.txt">Table of n, a(n) for n = 0..1000</a>

%H Luciano Ancora, <a href="/A254369/a254369.pdf">Demonstration of formulas</a>, page 2.

%H Luciano Ancora, <a href="/A254369/a254369_1.pdf">Recurrence relations for partial sums of m-th powers</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).

%F G.f.: -2*(533*x^3-638*x^2+238*x-28) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - _Colin Barker_, Jan 30 2015

%F a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - _Colin Barker_, Jan 30 2015

%t Table[15 2^n + 4^n + 5 3^n + 35, {n, 0, 30}] (* _Bruno Berselli_, Jan 30 2015 *)

%t LinearRecurrence[{10,-35,50,-24},{56,84,156,354},30] (* _Harvey P. Dale_, Dec 04 2020 *)

%o (PARI) vector(30, n, n--; 15*2^n + 4^n + 5*3^n + 35) \\ _Colin Barker_, Jan 30 2015

%Y Cf. A168614, A254368, A254370.

%K nonn,easy

%O 0,1

%A _Luciano Ancora_, Jan 29 2015