A035329 a(n) = n*(2*n+5)*(2*n+7).

0, 63, 198, 429, 780, 1275, 1938, 2793, 3864, 5175, 6750, 8613, 10788, 13299, 16170, 19425, 23088, 27183, 31734, 36765, 42300, 48363, 54978, 62169, 69960, 78375, 87438, 97173, 107604, 118755, 130650, 143313, 156768, 171039, 186150, 202125, 218988, 236763

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• Eric Harold Neville, Jacobian Elliptic Functions, 2nd ed., p. 38.

Links

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

Crossrefs

Cf. A020742, A033537.

Programs

Magma

[n*(2*n+5)*(2*n+7) : n in [0..60]]; // Wesley Ivan Hurt, Oct 05 2020

Mathematica

Table[n*(2*n + 5)*(2*n + 7), {n, 0, 60}] (* Wesley Ivan Hurt, Oct 05 2020 *)

PARI

a(n)=n*(2*n+5)*(2*n+7) \\ Charles R Greathouse IV, Oct 18 2022

Formula

From Wesley Ivan Hurt, Oct 05 2020: (Start)

a(n) = 4*n^3 + 24*n^2 + 35*n.

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

G.f.: 3*x*(21-18*x+5*x^2)/(1-x)^4. (End)

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

E.g.f.: exp(x)*x*(63 + 36*x + 4*x^2).

a(n) = A033537(n)*A020742(n). (End)

Extensions

More terms from Sean A. Irvine, Oct 05 2020