A283551 a(n) = -1 + 5*n/6 + n^3/6.

-1, 0, 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, 297, 376, 468, 574, 695, 832, 986, 1158, 1349, 1560, 1792, 2046, 2323, 2624, 2950, 3302, 3681, 4088, 4524, 4990, 5487, 6016, 6578, 7174, 7805, 8472, 9176, 9918, 10699, 11520, 12382, 13286, 14233, 15224, 16260

Offset: 0

Author

Paul Curtz, Mar 10 2017

Keywords

• sign
• easy
• less

Comments

Essentially a duplicate of A003600.

Examples

			G.f. = -1 + 2*x^2 + 6*x^3 + 13*x^4 + 24*x^5 + 40*x^6 + 62*x^7 + ... - _Michael Somos_, Jul 07 2022
		

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).

Crossrefs

Essentially a duplicate of A003600.

Programs

Magma

[-1 + 5*n/6 + n^3/6 : n in [0..60]]; // Wesley Ivan Hurt, Oct 03 2017

Maple

A283551:=n->-1 + 5*n/6 + n^3/6: seq(A283551(n), n=0..100); # Wesley Ivan Hurt, Oct 03 2017

Mathematica

Table[-1 + 5 n/6 + n^3/6, {n, 0, 39}] (* Michael De Vlieger, Mar 15 2017 *)

SageMath

def A283551(n): return (n^3 +5*n -6)//6
print([A283551(n) for n in range(61)]) # G. C. Greubel, Apr 18 2025

Formula

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

a(n) = a(n-1) + A000124(n).

G.f.: -(1 - 4*x + 4*x^2 - 2*x^3)/(1-x)^4. - Robert G. Wilson v, Mar 15 2017

E.g.f.: (1/6)*(-6 + 6*x + 3*x^2 + x^3)*exp(x). - G. C. Greubel, Apr 18 2025

Extensions

Corrected by Jeremy Gardiner, Jan 29 2019