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%I #20 Sep 08 2022 08:45:32
%S 4,16,84,496,3108,20176,134004,903856,6161988,42326416,292299924,
%T 2026332016,14085959268,98111307856,684331371444,4778093436976,
%U 33385561506948,233393582580496,1632228682596564,11417969833962736
%N a(n) = 1^n + 3^n + 5^n + 7^n.
%H Vincenzo Librandi, <a href="/A134006/b134006.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (16, -86, 176, -105).
%F a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3) - 48.
%F a(n) = A074507(n) + A000420(n). - _Michel Marcus_, Nov 07 2013
%F G.f.: 1 / (1 - x) + 1 / (1 - 3*x) + 1 / (1 - 5*x) + 1 / (1 - 7*x), E.g.f.: exp(x) + exp(3*x) + exp(5*x) + exp(7*x). - _Michael Somos_, Jun 29 2017
%e a(3)=84 because 1^2+3^2+5^2+7^2=84.
%t Table[1^n+3^n+5^n+7^n,{n,0,30}]
%o (Magma) [1^n + 3^n + 5^n + 7^n: n in [0..30]]; // _Vincenzo Librandi_, Jun 20 2011
%o (PARI) {a(n) = 1^n + 3^n + 5^n + 7^n}; /* _Michael Somos_, Jun 29 2017 */
%Y Cf. A034472, A074507, A134007.
%K nonn
%O 0,1
%A _Artur Jasinski_, Oct 01 2007