A033591 a(n) = (2*n+1)*(3*n+1)*(4*n+1).

1, 60, 315, 910, 1989, 3696, 6175, 9570, 14025, 19684, 26691, 35190, 45325, 57240, 71079, 86986, 105105, 125580, 148555, 174174, 202581, 233920, 268335, 305970, 346969, 391476, 439635, 491590, 547485

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(0)=1, a(1)=60, a(2)=315, a(3)=910. - Harvey P. Dale, Oct 24 2014

G.f.: (1 + 56*x + 81*x^2 + 6*x^3)/(1-x)^4. - R. J. Mathar, Feb 06 2017

From G. C. Greubel, Mar 05 2020: (Start)

a(n) = n^2 * Pochhammer(2+1/n, 3).

E.g.f.: (1 + 59*x + 98*x^2 + 24*x^3)*exp(x). (End)

Maple

seq( (2*n+1)*(3*n+1)*(4*n+1), n=0..30); # G. C. Greubel, Mar 05 2020

Mathematica

Table[(2n+1)(3n+1)(4n+1), {n, 0, 30}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 60, 315, 910}, 30] (* Harvey P. Dale, Oct 24 2014 *)

Prog

(PARI) vector(31, n, my(m=n-1); (2*m+1)*(3*m+1)*(4*m+1)) \\ G. C. Greubel, Mar 05 2020
(Magma) [(2*n+1)*(3*n+1)*(4*n+1): n in [0..30]]; // G. C. Greubel, Mar 05 2020
(Sage) [(2*n+1)*(3*n+1)*(4*n+1) for n in (0..30)] # G. C. Greubel, Mar 05 2020

Crossrefs

Sequence in context: A298045 A063497 A096363 * A133118 A211336 A092478

Adjacent sequences: A033588 A033589 A033590 * A033592 A033593 A033594

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved