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

0,3

Comments

Exponents are prime numbers in decreasing order.

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).

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

Example

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

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 *)

Prog

(Magma) [n^5-n^3-n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
(PARI) for(n=0, 50, print1(n^5 - n^3 - n^2, ", ")) \\ G. C. Greubel, Oct 20 2017

Crossrefs

Cf. A000290, A000578, A000584, A011379, A045991, A100019.

Cf. A133071, A133072, A133073.

Sequence in context: A334692 A325474 A364651 * A135179 A220939 A231059

Adjacent sequences: A133067 A133068 A133069 * A133071 A133072 A133073

Keyword

sign,easy

Author

Omar E. Pol, Nov 01 2007

Extensions

More terms from Vincenzo Librandi, Dec 15 2010

Status

approved