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A140163 a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n if n is even.

%I A140163 #24 Jan 02 2024 09:02:50
%S A140163 1,3,246,250,3375,3381,20188,20196,79245,79255,240306,240318,611611,
%T A140163 611625,1371000,1371016,2790873,2790891,5266990,5267010,9351111,
%U A140163 9351133,15787476,15787500,25553125,25553151,39902058,39902086,60413235
%N A140163 a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n if n is even.
%H A140163 G. C. Greubel, <a href="/A140163/b140163.txt">Table of n, a(n) for n = 1..1000</a>
%H A140163 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6, -1,1).
%F A140163 G.f.: -x*(1 + 2*x + 237*x^2 - 8*x^3 + 1682*x^4 + 12*x^5 + 1682*x^6 - 8*x^7 + 237*x^8 + 2*x^9 + x^10)/((1+x)^6*(x-1)^7). - _R. J. Mathar_, Feb 22 2009
%F A140163 a(n) = (1/24)*(n + n^2)*(6*(1 + (-1)^n) - (1 - 9*(-1)^n)*n + (1 - 9*(-1)^n)*n^2 + (4 - 6*(-1)^n)*n^3 + 2*n^4). - _G. C. Greubel_, Jul 05 2018
%p A140163 a:=proc(n) option remember: if n=1 then 1 elif modp(n,2)<>0 then procname(n-1)+n^5 else procname(n-1)+n; fi: end; seq(a(n),n=1..30); # _Muniru A Asiru_, Jul 07 2018
%t A140163 Table[(1/24)*(n +n^2)*(6*(1 +(-1)^n) - (1-9*(-1)^n)*n + (1 -9*(-1)^n)*n^2 + (4 -6*(-1)^n)*n^3 + 2*n^4), {n, 1, 50}] (* or *) LinearRecurrence[{1, 6, -6, -15, 15, 20, -20, -15, 15, 6, -6, -1, 1}, {1, 3, 246, 250, 3375, 3381, 20188, 20196, 79245, 79255, 240306, 240318, 611611}, 60] (* _G. C. Greubel_, Jul 05 2018 *)
%o A140163 (PARI) for(n=1,50, print1((1/24)*(n +n^2)*(6*(1 +(-1)^n) - (1-9*(-1)^n)*n + (1 -9*(-1)^n)*n^2 + (4 -6*(-1)^n)*n^3 + 2*n^4), ", ")) \\ _G. C. Greubel_, Jul 05 2018
%o A140163 (Magma) [(1/24)*(n +n^2)*(6*(1 +(-1)^n) - (1-9*(-1)^n)*n + (1 -9*(-1)^n)*n^2 + (4 -6*(-1)^n)*n^3 + 2*n^4): n in [1..50]]; // _G. C. Greubel_, Jul 05 2018
%Y A140163 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140163 nonn
%O A140163 1,2
%A A140163 _Artur Jasinski_, May 12 2008