A242477 a(n) = floor(3*n^2/4).

0, 0, 3, 6, 12, 18, 27, 36, 48, 60, 75, 90, 108, 126, 147, 168, 192, 216, 243, 270, 300, 330, 363, 396, 432, 468, 507, 546, 588, 630, 675, 720, 768, 816, 867, 918, 972, 1026, 1083, 1140, 1200, 1260, 1323, 1386, 1452, 1518, 1587, 1656, 1728, 1800, 1875

Offset: 0

Author

Vincenzo Librandi, May 22 2014

Keywords

• nonn
• easy

Comments

The even-numbered terms are the same as the three - quarter squares; the odd-numbered terms are one less.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Craig Knecht, Maximum number of octiamonds in a hexagon.
• Robert Munafo, Sequence MCS429697.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A002620.

Programs

Magma

[Floor(3*n^2/4): n in [0..60]];

Mathematica

Table[Floor[3 n^2/4], {n, 0, 60}]
LinearRecurrence[{2,0,-2,1},{0,0,3,6},60] (* Harvey P. Dale, Sep 07 2019 *)

Sage

[3*floor(n^2/4) for n in (0..60)] # Bruno Berselli, May 22 2014

Formula

a(n) = a(n-2) + 3*(n-1) for n>1, a(0) = a(1) = 0.

From Bruno Berselli, May 22 2014: (Start)

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

a(n) = 3*A002620(n). (End)

Sum_{n>=2} 1/a(n) = Pi^2/18 + 1/3. - Amiram Eldar, Feb 16 2023