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%I #27 Jun 03 2024 18:42:13
%S 1,11,67,383,1669,6275,23431,94967,423433,2012219,9865675,48989231,
%T 244389517,1221074483,6104053519,30518337575,152588939281,
%U 762940873067,3814699155283,19073488804319,95367434840725,476837162287331,2384185796169367,11920928961514583
%N a(n) = n^5 + 5*n + 5^n.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (11,-45,95,-115,81,-31,5).
%F a(n) = A000584(n) + A008587(n) + A000351(n).
%F G.f.: (29*x^6+30*x^5+459*x^4-46*x^3+9*x^2-1) / ((x-1)^6*(5*x-1)). - _Colin Barker_, May 09 2013
%e a(1) = 1^5 + 5*1 + 5^1 = 11.
%e a(2) = 2^5 + 5*2 + 5^2 = 67.
%t Table[n^5 + 5*n + 5^n, {n, 0, 30}] (* _T. D. Noe_, Dec 17 2012 *)
%t LinearRecurrence[{11,-45,95,-115,81,-31,5},{1,11,67,383,1669,6275,23431},30] (* _Harvey P. Dale_, Jun 03 2024 *)
%o (Maxima) makelist(n^5 + 5*n + 5^n,n,0,20); /* _Martin Ettl_, Jan 15 2013 */
%o (PARI) a(n)=n^5+5*n+5^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000351, A000584, A008587, A220425, A220509.
%K nonn,easy
%O 0,2
%A _Jonathan Vos Post_, Dec 15 2012