A119536 a(n) = 3*n^3 + 3*n.

0, 6, 30, 90, 204, 390, 666, 1050, 1560, 2214, 3030, 4026, 5220, 6630, 8274, 10170, 12336, 14790, 17550, 20634, 24060, 27846, 32010, 36570, 41544, 46950, 52806, 59130, 65940, 73254, 81090, 89466, 98400, 107910, 118014, 128730, 140076, 152070, 164730, 178074, 192120

Offset

0,2

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = 3*A034262(n) = 6*A006003(n). - J. M. Bergot, Apr 16 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=6, a(2)=30, a(3)=90. - Harvey P. Dale, Mar 19 2013

From Elmo R. Oliveira, May 22 2026: (Start)

G.f.: 6*x*(1 + x + x^2)/(1 - x)^4.

E.g.f.: 3*x*(x + 1)*(x + 2)*exp(x).

a(n) = A008530(n)/2 for n > 0. (End)

Maple

[seq (3*n^3+3*n, n=0..60)];

Mathematica

Table[3n^3+3n, {n, 0, 40}] (* Harvey P. Dale, Mar 19 2013 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {0, 6, 30, 90}, 40] (* Harvey P. Dale, Mar 19 2013 *)

Crossrefs

Cf. A006003, A008530, A034262.

Sequence in context: A217260 A009775 A297570 * A107394 A033487 A061138

Adjacent sequences: A119533 A119534 A119535 * A119537 A119538 A119539

Keyword

easy,nonn

Author

Zerinvary Lajos, May 28 2006

Extensions

More terms from Elmo R. Oliveira, May 22 2026

Status

approved