A355552 Number of ways to select 3 or more collinear points from a 4 X n grid.

5, 10, 23, 54, 117, 240, 497, 1006, 2027, 4074, 8169, 16356, 32741, 65506, 131039, 262110, 524253, 1048536, 2097113, 4194262, 8388563, 16777170, 33554385, 67108812, 134217677, 268435402, 536870855, 1073741766, 2147483589, 4294967232, 8589934529, 17179869118, 34359738299

Offset: 1

Author

Thomas Garrison, Jul 14 2022

Keywords

• nonn
• easy

Links

• Lucas A. Brown, Table of n, a(n) for n = 1..1000
• Lucas A. Brown, A355552.py
• Index entries for linear recurrences with constant coefficients, signature (2,1,-1,-2,-1,2).

Crossrefs

Cf. A000982 (1 X n), 2*A000982 (2 X n), A355553 (n X n).

Formula

a(n) == H(n) + 3 * D4(n) + 2 * E(n), where

H(n) == 2^(n+2) - 4 - 2*n*(n+1),

D4(n) == floor((n^2 + 2) / 3), and

E(n) == floor((n^2 + 1) / 2).

a(n) ~ 2^(n+2).

G.f.: -x * (6x^4 + 3x^3 - 2x^2 + 5) / ( (x - 1)^2 * (2x^2 + x - 1) * (x^2 + x + 1) ). - Lucas A. Brown, Oct 22 2022

Extensions

Corrected and extended by Lucas A. Brown, Oct 20 2022