A061167 a(n) = n^5 - n.

0, 0, 30, 240, 1020, 3120, 7770, 16800, 32760, 59040, 99990, 161040, 248820, 371280, 537810, 759360, 1048560, 1419840, 1889550, 2476080, 3199980, 4084080, 5153610, 6436320, 7962600, 9765600, 11881350, 14348880, 17210340, 20511120, 24299970, 28629120

Offset: 0

Author

Henry Bottomley, Apr 18 2001

Keywords

• easy
• nonn

Comments

(b^2+c^2)/(bc+1) is an integer if {b,c} are of the form {0,n}, {n,n^3}, {n^3,n^5-n}, {n^5-n,n^7-2n^3}, {n^7-2n^3,n^9-3n^5+n}, etc. for some n, in which case the division results in n^2. Cf. A052530.

Convolution of A033429 by A033581. - R. J. Mathar, Aug 19 2008

Examples

			a(2) = 32 - 2 = 30.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• D. Zagier, Problems posed at the St Andrews Colloquium, 1996
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Subsequence of A249674.

Cf. A000584, A024002, A033429, A033455, A033581, A052530.

Programs

Magma

[n^5-n: n in [0..40]]; // Vincenzo Librandi, May 02 2011

Mathematica

Table[n^5 - n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)

Formula

a(n) = 30*A033455(n-1). [Corrected by Bernard Schott, Mar 16 2021]

a(n) = -n*A024002(n).

a(n) = A000584(n) - n.

O.g.f.: 30x^2(1+x)^2/(1-x)^6. - R. J. Mathar, Aug 19 2008

a(n) = n * (n-1) * (n+1) * (n^2+1). - Bernard Schott, Mar 16 2021

E.g.f.: exp(x)*x^2*(15 + 25*x + 10*x^2 + x^3). - Stefano Spezia, Dec 27 2021