Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Sep 08 2022 08:45:28
%S -1,-4,1,122,683,2344,6221,14006,28087,51668,88889,144946,226211,
%T 340352,496453,705134,978671,1331116,1778417,2338538,3031579,3879896,
%U 4908221,6143782,7616423,9358724,11406121,13797026,16572947,19778608,23462069,27674846,32472031,37912412,44058593
%N a(n) = n^5-n^4-n^3-n^2-n-1.
%C More generally, the ordinary generating function for the values of quintic polynomial b*n^5 + p*n^4 + q*n^3 + k*n^2 + m*n + r, is (r + (b + p + q + k + m - 5*r)*x + (13*b + 5*p + q - k - 2*m + 5*r)*2*x^2 + (33*b - 3*q + 3*m - 5*r)*2*x^3 + (26*b - 10*p + 2*q + 2*k - 4*m + 5*r)*x^4 + (b - p + q - k + m - r)*x^5)/(1 - x)^6. - _Ilya Gutkovskiy_, Mar 31 2016
%H Vincenzo Librandi, <a href="/A125083/b125083.txt">Table of n, a(n) for n = 0..580</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1)
%F G.f.: (-1 + 2*x + 10*x^2 + 76*x^3 + 31*x^4 + 2*x^5)/(1 - x)^6. - _Ilya Gutkovskiy_, Mar 31 2016
%t Table[n^5 - n^4 - n^3 - n^2 - n - 1, {n, 0, 41}]
%o (Magma) [n^5-n^4-n^3-n^2-n-1: n in [0..60]]; // _Vincenzo Librandi_, Apr 26 2011
%o (PARI) a(n) = n^5-n^4-n^3-n^2-n-1; \\ _Michel Marcus_, Mar 31 2016
%Y Cf. A125082, A083074.
%K sign,easy
%O 0,2
%A _Artur Jasinski_, Nov 19 2006