A334706 Number of collinear triples in a 4 X n rectangular grid.

4, 8, 20, 44, 84, 140, 224, 332, 472, 648, 864, 1120, 1428, 1784, 2196, 2668, 3204, 3804, 4480, 5228, 6056, 6968, 7968, 9056, 10244, 11528, 12916, 14412, 16020, 17740, 19584, 21548, 23640, 25864, 28224, 30720, 33364, 36152, 39092, 42188, 45444, 48860, 52448, 56204

Offset: 1

Author

N. J. A. Sloane, Jun 13 2020

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).

Crossrefs

A column of A334704.

Formula

From Stefano Spezia, Jun 20 2020: (Start)

G.f.: 4*x*(1 + x^2 + 2*x^3 + 2*x^4)/((1 - x)^4*(1 + 2*x + 2*x^2 + x^3)).

a(n) = 2*a(n-1) - a(n-3) - a(n-4) + 2*a(n-6) - a(n-7) for n > 7. (End)

Extensions

Terms a(8) and beyond from Giovanni Resta, Jun 20 2020