A125083 a(n) = n^5-n^4-n^3-n^2-n-1.

-1, -4, 1, 122, 683, 2344, 6221, 14006, 28087, 51668, 88889, 144946, 226211, 340352, 496453, 705134, 978671, 1331116, 1778417, 2338538, 3031579, 3879896, 4908221, 6143782, 7616423, 9358724, 11406121, 13797026, 16572947, 19778608, 23462069, 27674846, 32472031, 37912412, 44058593

Offset: 0

Author

Artur Jasinski, Nov 19 2006

Keywords

• sign
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..580
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1)

Crossrefs

Cf. A125082, A083074.

Programs

Magma

[n^5-n^4-n^3-n^2-n-1: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011

Mathematica

Table[n^5 - n^4 - n^3 - n^2 - n - 1, {n, 0, 41}]

PARI

a(n) = n^5-n^4-n^3-n^2-n-1; \\ Michel Marcus, Mar 31 2016

Formula

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