A060163 a(n) = (n^3 + 5*n + 18)/6.

0, 2, 3, 4, 6, 10, 17, 28, 44, 66, 95, 132, 178, 234, 301, 380, 472, 578, 699, 836, 990, 1162, 1353, 1564, 1796, 2050, 2327, 2628, 2954, 3306, 3685, 4092, 4528, 4994, 5491, 6020, 6582, 7178, 7809, 8476, 9180, 9922, 10703, 11524, 12386, 13290, 14237

Offset

-2,2

Comments

a(n) = (m^2 - 6*m + 17)*m/6 where m = n+2. - Frank Ellermann

Links

Harry J. Smith, Table of n, a(n) for n = -2..1000

Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4.

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

Formula

a(n) = a(n-1) + A000124(n-1) = A060162(n+3, n) = A004006(n)+3 = A000125(n) + 2.

It appears that a(n) = A011826(n+1) + 1.

a(n) = n + 2 + binomial(n,3) (with different offset). - Zerinvary Lajos, Jul 23 2006

G.f.: (2 - 5*x + 4*x^2)/(x*(1 - x)^4). - Stefano Spezia, Nov 19 2023

Maple

seq((n^3 + 5*n + 18)/6, n=-2..46); # Zerinvary Lajos, Jul 23 2006

Mathematica

a=2; s=3; lst={-3, -1, 0, 1, s}; Do[a+=n; s+=a; AppendTo[lst, s], {n, 2, 6!, 1}]; lst+3 (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)
Table[(n^3+5n+18)/6, {n, -2, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 2, 3, 4}, 50] (* Harvey P. Dale, Mar 11 2015 *)

Prog

(PARI) { for (n=-2, 1000, write("b060163.txt", n, " ", (n^3 + 5*n + 18)/6); ) } \\ Harry J. Smith, Jul 02 2009
(Magma) [(n^3+5*n+18)/6 : n in [-2..50]]; // Wesley Ivan Hurt, Mar 25 2020

Crossrefs

Cf. A000124, A000125, A004006, A011826, A060162.

Sequence in context: A293632 A216783 A026502 * A106511 A024490 A317200

Adjacent sequences: A060160 A060161 A060162 * A060164 A060165 A060166

Keyword

easy,nonn

Author

Henry Bottomley, Mar 13 2001

Status

approved