A006124 a(n) = 3 + n/2 + 7*n^2/2.

3, 7, 18, 36, 61, 93, 132, 178, 231, 291, 358, 432, 513, 601, 696, 798, 907, 1023, 1146, 1276, 1413, 1557, 1708, 1866, 2031, 2203, 2382, 2568, 2761, 2961, 3168, 3382, 3603, 3831, 4066, 4308, 4557, 4813, 5076, 5346, 5623, 5907, 6198, 6496, 6801, 7113, 7432, 7758

Offset

0,1

Comments

Numbers k such that 56*k - 167 is a square. - Klaus Purath, Feb 05 2026

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Jonathan L. King, Brick tiling and monotone Boolean functions, Part 1 and Part 2.

Jonathan L. King, A change-of-coordinates from Geometry to Algebra, applied to Brick Tilings, arXiv:math/9809176 [math.CO], 1998, page 10, row 3 of the table.

C. L. Mallows & N. J. A. Sloane, Emails, May 1991.

C. L. Mallows & N. J. A. Sloane, Emails, Jun. 1991.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Vincenzo Librandi, Jul 07 2012: (Start)

G.f.: (3 - 2*x + 6*x^2)/(1-x)^3.

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

a(n) = 3 + A022265(n). - R. J. Mathar, Jan 12 2024

E.g.f.: exp(x)*(6 + 8*x + 7*x^2)/2. - Elmo R. Oliveira, Dec 28 2024

From Klaus Purath, Feb 05 2026: (Start)

a(n) = 2*a(n-1) - a(n-2) + 7.

a(n) = a(n-1) + 7*n - 3. (End)

Mathematica

Table[3+n/2+7/2 n^2, {n, 0, 50}]  (* Harvey P. Dale, Mar 21 2011 *)
CoefficientList[Series[(3-2*x+6*x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)

Prog

(Magma) I:=[3, 7, 18]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jul 07 2012
(PARI) a(n)=3+n/2+7*n^2/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A022265.

Sequence in context: A308445 A328653 A011799 * A197182 A074587 A208715

Adjacent sequences: A006121 A006122 A006123 * A006125 A006126 A006127

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved