A133070 a(n) = n^5 - n^3 - n^2.

0, -1, 20, 207, 944, 2975, 7524, 16415, 32192, 58239, 98900, 159599, 246960, 368927, 534884, 755775, 1044224, 1414655, 1883412, 2468879, 3191600, 4074399, 5142500, 6423647, 7948224, 9749375, 11863124, 14328495, 17187632, 20485919, 24272100, 28598399, 33520640, 39098367, 45394964

Offset: 0

Author

Omar E. Pol, Nov 01 2007

Keywords

• sign
• easy

Comments

Exponents are prime numbers in decreasing order.

Examples

			a(7)=16415 because 7^5=16807, 7^3=343, 7^2=49 and we can write 16807-343-49=16415.
		

Links

• G. C. Greubel, 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. A000290, A000578, A000584, A011379, A045991, A100019.

Cf. A133071, A133072, A133073.

Programs

Magma

[n^5-n^3-n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010

Mathematica

Table[n^5-n^3-n^2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,-1,20,207,944,2975},41] (* Harvey P. Dale, Jul 23 2011 *)

PARI

for(n=0,50, print1(n^5 - n^3 - n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Formula

a(n) = n^5 - n^3 - n^2.

G.f.: x*(-1 +26*x + 72*x^2 + 22*x^3 + x^4)/(1-x)^6. - R. J. Mathar, Nov 14 2007

a(n) = 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6), with a(0)=0, a(1)=-1, a(2)=20, a(3)=207, a(4)=944, a(5)=2975. - Harvey P. Dale, Jul 23 2011

Extensions

More terms from Vincenzo Librandi, Dec 15 2010