A017454 a(n) = (11*n + 5)^6.

15625, 16777216, 387420489, 3010936384, 13841287201, 46656000000, 128100283921, 304006671424, 646990183449, 1265319018496, 2313060765625, 4001504141376, 6611856250609, 10509215371264, 16157819263041, 24137569000000, 35161828327081, 50096498540544, 69980368892329

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), this sequence (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

Programs

GAP

List([0..20], n-> (11*n+5)^6); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+5)^6: n in [0..20]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq((11*n+5)^6, n=0..20); # G. C. Greubel, Sep 18 2019

Mathematica

(11*Range[0,30]+5)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {15625, 16777216, 387420489, 3010936384, 13841287201, 46656000000, 128100283921}, 30] (* Harvey P. Dale, Dec 12 2013 *)

PARI

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

Sage

[(11*n+5)^6 for n in (0..20)] # G. C. Greubel, Sep 18 2019

Formula

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); a(0)=15625, a(1)=16777216, a(2)=387420489, a(3)=3010936384, a(4)=13841287201, a(5)=46656000000, a(6)=128100283921. - Harvey P. Dale, Dec 12 2013

From G. C. Greubel, Sep 18 2019: (Start)

G.f.: (15625 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 +46656*x^6)/(1-x)^7.

E.g.f.: (15625 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 +1771561*x^6)*exp(x). (End)