A001509 a(n) = (5*n + 1)*(5*n + 2)*(5*n + 3).

6, 336, 1716, 4896, 10626, 19656, 32736, 50616, 74046, 103776, 140556, 185136, 238266, 300696, 373176, 456456, 551286, 658416, 778596, 912576, 1061106, 1224936, 1404816, 1601496, 1815726, 2048256, 2299836, 2571216, 2863146, 3176376, 3511656, 3869736, 4251366

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy
• changed

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).

Crossrefs

Cf. A001622, A016861, A016873, A016885.

Programs

Maple

A001509:=n->(5*n+1)*(5*n+2)*(5*n+3); seq(A001509(n), n=0..50); # Wesley Ivan Hurt, May 07 2014

Mathematica

Table[(5*n + 1)*(5*n + 2)*(5*n + 3), {n, 0, 100}] (* Harvey P. Dale, Apr 21 2011 *)

Formula

a(n) = A016861(n) * A016873(n) * A016885(n). - Wesley Ivan Hurt, May 07 2014

G.f.: 6*(1 + 52*x + 68*x^2 + 4*x^3)/(1 - x)^4. - Stefano Spezia, Jan 03 2023

Sum_{n>=0} 1/a(n) = sqrt(2*(25-11*sqrt(5))/5)*Pi/20 + log(phi)/(2*sqrt(5)), where phi is the golden ratio (A001622). - Amiram Eldar, Jan 26 2023

From Elmo R. Oliveira, Sep 07 2025: (Start)

E.g.f.: exp(x)*(6 + 330*x + 525*x^2 + 125*x^3).

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