A017442 a(n) = (11*n + 4)^6.

4096, 11390625, 308915776, 2565726409, 12230590464, 42180533641, 117649000000, 282429536481, 606355001344, 1194052296529, 2194972623936, 3814697265625, 6327518887936, 10090298369529, 15557597153344

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Powers of the form (11*n+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), this sequence (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

Programs

GAP

List([0..20], n-> (11*n+4)^6); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+4)^6: n in [0..20]]; // G. C. Greubel, Sep 18 2019

Maple

A017442:=n->(11*n+4)^6; seq(A017442(n), n=0..20); # Wesley Ivan Hurt, Nov 11 2013

Mathematica

(11*Range[0,20]+4)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {4096, 11390625, 308915776, 2565726409, 12230590464, 42180533641, 117649000000}, 20] (* Harvey P. Dale, Feb 18 2012 *)

PARI

vector(20, n, (11*n-7)^6) \\ G. C. Greubel, Sep 18 2019

Sage

[(11*n+4)^6 for n in (0..20)] # G. C. Greubel, Sep 18 2019

Formula

From Harvey P. Dale, Feb 18 2012: (Start)

a(0)=4096, a(1)=11390625, a(2)=308915776, a(3)=2565726409, a(4)=12230590464, a(5)=42180533641, a(6)=117649000000, a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) - 35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7).

G.f.: ((x*(x*(x*(x*(x*(117649*x [phone]) [phone]) [phone]) [phone]) [phone]) +4096)/(1-x)^7). (End)

a(n) = A017437(n)^6. - Michel Marcus, Nov 12 2013

E.g.f.: (4096 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 +1771561*x^6)*exp(x). - G. C. Greubel, Sep 18 2019