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A355552
Number of ways to select 3 or more collinear points from a 4 X n grid.
3
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
1,1
LINKS
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
CROSSREFS
Cf. A000982 (1 X n), 2*A000982 (2 X n), A355553 (n X n).
Sequence in context: A257464 A295731 A175661 * A197174 A098112 A237435
KEYWORD
nonn,easy
AUTHOR
Thomas Garrison, Jul 14 2022
EXTENSIONS
Corrected and extended by Lucas A. Brown, Oct 20 2022
STATUS
approved