A001505 a(n) = (4*n+1)*(4*n+2)*(4*n+3).

6, 210, 990, 2730, 5814, 10626, 17550, 26970, 39270, 54834, 74046, 97290, 124950, 157410, 195054, 238266, 287430, 342930, 405150, 474474, 551286, 635970, 728910, 830490, 941094, 1061106, 1190910, 1330890, 1481430, 1642914, 1815726, 2000250, 2196870, 2405970

Offset

0,1

Links

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

L. B. W. Jolley, Summation of Series, Dover, 1961.

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

Formula

a(n) = 6*A015219(n).

Sum_{n>=0} 1/a(n) = log(2)/4 = 0.17328679513998... [Jolley eq. 253. Typo fixed by Jaume Oliver Lafont, Jan 09 2009]

G.f.: 6*(1+x)*(x^2+30*x+1)/(x-1)^4. - R. J. Mathar, Apr 02 2011

Sum_{n>=0} (-1)^n/a(n) = (sqrt(2)-1)*Pi/8. - Amiram Eldar, Sep 17 2022

E.g.f.: 2*exp(x)*(3 + 102*x + 144*x^2 + 32*x^3). - Stefano Spezia, Aug 24 2025

From Elmo R. Oliveira, Sep 08 2025: (Start)

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

a(n) = A004767(n)*A157870(n) = A054777(n+1)/A008586(n+1). (End)

Mathematica

Table[(4n+1)(4n+2)(4n+3), {n, 0, 49}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

Prog

(Magma) [(4*n+1)*(4*n+2)*(4*n+3): n in [0..100]]; // Vincenzo Librandi, Apr 04 2011
(PARI) a(n)=(4*n+1)*(4*n+2)*(4*n+3) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A004767, A008586, A015219, A054777, A157870.

Sequence in context: A094805 A055193 A346015 * A327248 A084694 A285149

Adjacent sequences: A001502 A001503 A001504 * A001506 A001507 A001508

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved