A191012 a(n) = n^5 - n^4 + n^3 - n^2 + n.

0, 1, 22, 183, 820, 2605, 6666, 14707, 29128, 53145, 90910, 147631, 229692, 344773, 501970, 711915, 986896, 1340977, 1790118, 2352295, 3047620, 3898461, 4929562, 6168163, 7644120, 9390025, 11441326, 13836447, 16616908, 19827445

Offset: 0

Author

Franz Vrabec, Jun 16 2011

Keywords

• easy
• nonn

Comments

n such that x^5 + x^4 + x^3 + x^2 + x + n factors over the integers.

Examples

			a(2) = 22 is in the sequence, because x^5 + x^4 + x^3 + x^2 + x + 22 = (x+2)*(x^4 - x^3 + 3*x^2 - 5*x + 11).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A060884.

Programs

Magma

[n^5 - n^4 + n^3 - n^2 + n: n in [0..30]]; // Vincenzo Librandi, Jun 18 2011

Maple

[seq(n*(n^4-n^3+n^2-n+1),n=0..25)];

PARI

a(n)=((((n-1)*n+1)*n-1)*n+1)*n \\ Charles R Greathouse IV, Jun 17 2011

Formula

a(n) = n*A060884(n).

G.f.: x*(5*x^4 + 32*x^3 + 66*x^2 + 16*x + 1)/(1-x)^6.