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%I #12 Sep 08 2022 08:45:50
%S 3,7,12,18,29,41,54,68,87,107,128,150,177,205,234,264,299,335,372,410,
%T 453,497,542,588,639,691,744,798,857,917,978,1040,1107,1175,1244,1314,
%U 1389,1465,1542,1620,1703,1787,1872,1958,2049,2141,2234,2328,2427,2527
%N Partial sums of numbers congruent to {3, 4, 5, 6} mod 8 (A047425).
%H G. C. Greubel, <a href="/A171835/b171835.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).
%F a(n) = Sum_{i=1..n} A047425(i).
%F From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F G.f.: x*(3+x+x^2+x^3+2*x^4)/((1-x)^3*(1+x+x^2+x^3)).
%F a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6.
%F a(n) = (4*n^2+2*n+5-2*I^(-n)-2*I^n-I^(2*n))/4 where I=sqrt(-1). (End)
%p A171835:=n->(4*n^2+2*n+5-2*I^(-n)-2*I^n-I^(2*n))/4: seq(A171835(n), n=1..80); # _Wesley Ivan Hurt_, Jun 04 2016
%t CoefficientList[Series[(3 + x + x^2 + x^3 + 2*x^4)/((1 - x)^3*(1 + x + x^2 + x^3)), {x, 0, 80}], x] (* _Wesley Ivan Hurt_, Jun 04 2016 *)
%t Table[(4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4, {n, 1, 100}] (* _G. C. Greubel_, Sep 04 2018 *)
%o (PARI) vector(100, n, (4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4) \\ _G. C. Greubel_, Sep 04 2018
%o (Magma) C<I> := ComplexField(); [Round((4*n^2 +2*n +5 -2*(1 +(-1)^n)*I^n -(-1)^n)/4): n in [1..100]]; // _G. C. Greubel_, Sep 04 2018
%Y Cf. A047425.
%K nonn,easy
%O 1,1
%A _Jaroslav Krizek_, Dec 19 2009
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