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A175828 a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.

%I A175828 #30 Sep 08 2022 08:45:52
%S A175828 1,2,15,26,53,74,115,146,201,242,311,362,445,506,603,674,785,866,991,
%T A175828 1082,1221,1322,1475,1586,1753,1874,2055,2186,2381,2522,2731,2882,
%U A175828 3105,3266,3503,3674,3925,4106,4371,4562,4841,5042,5335,5546,5853,6074
%N A175828 a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.
%C A175828 a(n) == A068073(n) (mod 4).
%C A175828 a(h) == 0 (mod 11) for h = 11*(k-floor((k-1)/3))-2*(-1)^(k+floor(k/3)) (cf. A175833).
%H A175828 Bruno Berselli, <a href="/A175828/b175828.txt">Table of n, a(n) for n = 0..1000</a>
%H A175828 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A175828 G.f.: (1+x+11*x^2+9*x^3+2*x^4)/((1+x)^2*(1-x)^3).
%F A175828 a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>4.
%F A175828 a(n)-a(n-2)-(a(n-1)-a(n-3)) = 2*A010718(n-1) for n>2.
%F A175828 a(n)-a(n-2)+(a(n-1)-a(n-3)) = A142241(n-2) for n>2.
%t A175828 Table[(n (6 n + 1) + (n + 2) (-1)^n)/2, {n, 0, 50}]
%t A175828 CoefficientList[Series[(1 + x + 11 x^2 + 9 x^3 + 2 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 19 2013 *)
%t A175828 LinearRecurrence[{1,2,-2,-1,1},{1,2,15,26,53},70] (* _Harvey P. Dale_, Jul 03 2019 *)
%o A175828 (Magma) [(n*(6*n+1)+(n+2)*(-1)^n)/2: n in [0..50]];
%o A175828 (Magma) I:=[1,2,15,26,53]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Aug 19 2013
%Y A175828 Cf. A068073, A010718, A142241, A175833.
%K A175828 nonn,easy
%O A175828 0,2
%A A175828 _Bruno Berselli_, Sep 21 2010 - Sep 25 2010