A001561 a(n) = (7*n+3)*(7*n+5)*(7*n+6).

90, 1560, 6460, 16848, 34782, 62320, 101520, 154440, 223138, 309672, 416100, 544480, 696870, 875328, 1081912, 1318680, 1587690, 1891000, 2230668, 2608752, 3027310, 3488400, 3994080, 4546408, 5147442, 5799240, 6503860, 7263360, 8079798, 8955232, 9891720

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From G. C. Greubel, Apr 28 2019: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

G.f.: 2*(45 + 600*x + 380*x^2 + 4*x^3)/(1-x)^4.

E.g.f.: (90 + 1470*x + 1715*x^2 + 343*x^3)*exp(x). (End)

Mathematica

Table[(7*n+3)*(7*n+5)*(7*n+6), {n, 0, 40}] (* T. D. Noe, Aug 09 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {90, 1560, 6460, 16848}, 40] (* Harvey P. Dale, Sep 26 2021 *)

Prog

(PARI) a(n) = (7*n+3)*(7*n+5)*(7*n+6); \\ G. C. Greubel, Apr 28 2019
(Magma) [(7*n+3)*(7*n+5)*(7*n+6): n in [0..40]]; // G. C. Greubel, Apr 28 2019
(Sage) [(7*n+3)*(7*n+5)*(7*n+6) for n in range(40)] # G. C. Greubel, Apr 28 2019
(GAP) List([0..40], n-> (7*n+3)*(7*n+5)*(7*n+6)) # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A234983 A166817 A166799 * A296998 A060094 A201062

Adjacent sequences: A001558 A001559 A001560 * A001562 A001563 A001564

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved