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%I #21 Sep 08 2022 08:45:32
%S 6,36,286,2556,24310,240276,2437006,25173996,263567590,2787694596,
%T 29716508926,318719062236,3434943872470,37162689280116,
%U 403310957409646,4387917394947276,47836135613930950,522357603781540836
%N a(n) = 1^n + 3^n + 5^n + 7^n + 9^n + 11^n.
%H Vincenzo Librandi, <a href="/A134008/b134008.txt">Table of n, a(n) for n = 0..300</a>
%H T. A. Gulliver, <a href="http://www.m-hikari.com/imf-2010/61-64-2010/index.html">Divisibility of sums of powers of odd integers</a>, Int. Math. For. 5 (2010) 3059-3066, eq. 6.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (36,-505,3480,-12139,19524,-10395).
%F a(n) = 35*a(n-1) - 470*a(n-2) + 3010*a(n-3) - 9129*a(n-4) + 10395*a(n-5) - 3840.
%F G.f.: -2*(6*x-1)*(1627*x^4 - 1752*x^3 + 578*x^2 - 72*x + 3)/((-1+x)*(9*x-1)*(7*x-1)*(3*x-1)*(5*x-1)*(11*x-1)). - _R. J. Mathar_, Nov 14 2007
%F a(n) = 36*a(n-1) - 505*a(n-2) + 3480*a(n-3) - 12139*a(n-4) + 19524*a(n-5) - 10395*a(n-6); a(0)=6, a(1)=36, a(2)=286, a(3)=2556, a(4)=24310, a(5)=240276. - _Harvey P. Dale_, Apr 20 2015
%e a(3)=286 because 1^2 + 3^2 + 5^2 + 7^2 + 9^2 + 11^2 = 286.
%t Table[1^n+3^n+5^n+7^n+9^n+11^n,{n,0,30}]
%t Join[{6},Table[Total[Range[1,11,2]^n],{n,20}]] (* or *) LinearRecurrence[ {36,-505,3480,-12139,19524,-10395},{6,36,286,2556,24310,240276},20] (* _Harvey P. Dale_, Apr 20 2015 *)
%o (Magma) [1^n + 3^n + 5^n + 7^n + 9^n + 11^n: n in [0..20]]; // _Vincenzo Librandi_, Jun 20 2011
%Y Cf. A034472, A074507, A134006, A134007.
%K nonn
%O 0,1
%A _Artur Jasinski_, Oct 01 2007