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

%I A355552 #32 Jan 17 2023 04:35:14
%S A355552 5,10,23,54,117,240,497,1006,2027,4074,8169,16356,32741,65506,131039,
%T A355552 262110,524253,1048536,2097113,4194262,8388563,16777170,33554385,
%U A355552 67108812,134217677,268435402,536870855,1073741766,2147483589,4294967232,8589934529,17179869118,34359738299
%N A355552 Number of ways to select 3 or more collinear points from a 4 X n grid.
%H A355552 Lucas A. Brown, <a href="/A355552/b355552.txt">Table of n, a(n) for n = 1..1000</a>
%H A355552 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A355552.py">A355552.py</a>
%H A355552 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1,-2,-1,2).
%F A355552 a(n) == H(n) + 3 * D4(n) + 2 * E(n), where
%F A355552 H(n) == 2^(n+2) - 4 - 2*n*(n+1),
%F A355552 D4(n) == floor((n^2 + 2) / 3), and
%F A355552 E(n) == floor((n^2 + 1) / 2).
%F A355552 a(n) ~ 2^(n+2).
%F A355552 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
%Y A355552 Cf. A000982 (1 X n), 2*A000982 (2 X n), A355553 (n X n).
%K A355552 nonn,easy
%O A355552 1,1
%A A355552 _Thomas Garrison_, Jul 14 2022
%E A355552 Corrected and extended by _Lucas A. Brown_, Oct 20 2022