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a(n) = 6^n + n^6.
8

%I #31 Jan 07 2023 13:17:52

%S 1,7,100,945,5392,23401,93312,397585,1941760,10609137,61466176,

%T 364568617,2179768320,13065520825,78371693632,470196375201,

%U 2821126684672,16926683582305,101559990680640,609359787056377

%N a(n) = 6^n + n^6.

%H Vincenzo Librandi, <a href="/A001594/b001594.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (13,-63,161,-245,231,-133,43,-6).

%F G.f.: (1 - 6*x + 72*x^2 - 75*x^3 - 1475*x^4 - 1776*x^5 - 334*x^6 - 7*x^7)/((1-x)^7*(1-6*x)). - _Vincenzo Librandi_, Aug 28 2014

%p seq(seq(k^n+n^k, k=6..6), n=0..19); # _Zerinvary Lajos_, Jun 29 2007

%t Table[6^n + n^6, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 6 x + 72 x^2 - 75 x^3 - 1475 x^4 - 1776 x^5 - 334 x^6 - 7 x^7)/((1-x)^7 (1-6 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 28 2014 *)

%t LinearRecurrence[{13,-63,161,-245,231,-133,43,-6},{1,7,100,945,5392,23401,93312,397585},20] (* _Harvey P. Dale_, Jan 07 2023 *)

%o (PARI) a(n)=6^n+n^6 \\ _Charles R Greathouse IV_, Feb 14 2011

%o (Magma) [6^n+n^6: n in [0..30]]; // _Vincenzo Librandi_, Oct 27 2011

%o (Sage) [6^n+n^6 for n in (0..30)] # _Bruno Berselli_, Aug 28 2014

%Y Cf. sequences of the form k^n+n^k: A001580 (k=2), A001585 (k=3), A001589 (k=4), A001593 (k=5), this sequence (k=6), A001596 (k=7), A198401 (k=8), A185277 (k=9), A177068 (k=10), A177069 (k=11).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_