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%I #22 Sep 08 2022 08:45:38
%S 1,70,357,3366,7748,29597,51604,134113,203475,427344,596471,1094240,
%T 1444702,2413711,3062718,4778067,5884949,8712458,10485145,14894314,
%U 17595816,24172785,28127672,37588181,43189063,56391412,64105419,82063428,92438690,116334659
%N Values of (n^5+47*n)/48 as n ranges over the numbers that are == +-1 mod 6.
%C ((n^5+47n)/48)^2 is the sum of the squares of the n^2 integers from (n^4-24n^2-25)/48 to (n^4+24n^2-73)/48. For example, when n=5, 70^2 is the sum of the 25 squares of the integers from 0 to 24.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = a(n-1)+5*a(n-2)-5*a(n-3)-10*a(n-4)+10*a(n-5)+10*a(n-6)-10*a(n-7)-5*a(n-8)+5*a(n-9)+a(n-10)-a(n-11). [_R. J. Mathar_, May 21 2009]
%F G.f.: x*(1 +69*x +282*x^2 +2664*x^3 +2957*x^4 +7494*x^5 +2957*x^6 +2664*x^7 +282*x^8 +69*x^9 +x^10)/((1+x)^5*(x-1)^6). [_R. J. Mathar_, May 21 2009]
%F a(n) = ((2*n-1)*(81*n^4-162*n^3+144*n^2-63*n+58)+(135*n^4-270*n^3+210*n^2-75*n+26)*(-1)^n)/32. - _Tani Akinari_, Oct 25 2014
%t With[{nn=20},(#^5+47#)/48&/@Sort[Join[6Range[0,nn]+1,6Range[nn]-1]]] (* _Harvey P. Dale_, Nov 15 2011 *)
%o (Magma) [((2*n-1)*(81*n^4-162*n^3+144*n^2-63*n+58)+(135*n^4-270*n^3+210*n^2-75*n+26)*(-1)^n)/32: n in [1..30]]; // _Vincenzo Librandi_, Oct 25 2014
%Y Cf. A007310, A097812, A001032.
%K nonn,easy
%O 1,2
%A _Michael David Hirschhorn_, May 21 2009
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