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%I #17 Apr 05 2023 15:39:18
%S 1,10,5,136,13,666,25,2080,41,5050,61,10440,85,19306,113,32896,145,
%T 52650,181,80200,221,117370,265,166176,313,228826,365,307720,421,
%U 405450,481,524800,545,668746,613,840456,685,1043290,761,1280800,841,1556730,925,1875016,1013,2239786
%N Sum of next n numbers/n if n divides the sum else n times the sum of next n numbers.
%C Quasipolynomial of order 2 and degree 5. - _Charles R Greathouse IV_, Oct 14 2013
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-10,0,10,0,-5,0,1).
%F For even n, a(n) = A000217(n^2) = n^2*(n^2+1)/2; for odd n, a(n) = (n^2 + 1)/2.
%F Sum_{n>=1} 1/a(n) = 1 + Pi^2/12 - Pi*cosech(Pi). - _Amiram Eldar_, Aug 23 2022
%e The sequence is: 1/1, (2+3)*2, (4+5+6)/3, (7+8+9+10)*4, ...
%t LinearRecurrence[{0,5,0,-10,0,10,0,-5,0,1},{1,10,5,136,13,666,25,2080,41,5050},50] (* _Harvey P. Dale_, May 01 2020 *)
%t fix[c_]:=If[Mod[Total[c],Length[c]]==0,Total[c]/Length[c],Length[c] Total[c]]; fix/@With[ {nn=50},TakeList[ Range[(nn(nn+1))/2],Range[nn]]] (* _Harvey P. Dale_, Apr 05 2023 *)
%o (PARI) a(n) = if (n%2, (n^2+1)/2, n^2*(n^2+1)/2); \\ _Michel Marcus_, Aug 23 2022
%Y Cf. A000217, A037270, A001844.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Apr 26 2004
%E Edited and extended by _Max Alekseyev_, Apr 26 2009
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