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

1,1

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).

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)

a(n) = 2/3*n^3 - n^2/3 + 4/3*n + O(1). - Charles R Greathouse IV, May 31 2026

Mathematica

LinearRecurrence[{2, 0, -1, -1, 0, 2, -1}, {4, 8, 20, 44, 84, 140, 224}, 50] (* Paolo Xausa, Jun 13 2026 *)

Prog

(PARI) a(n)=(2*n^3-n^2+4*n+247608\8^(n%6)%8)/3 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

A column of A334704.

Sequence in context: A254128 A047196 A009889 * A095804 A084219 A394766

Adjacent sequences: A334703 A334704 A334705 * A334707 A334708 A334709

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 13 2020

Extensions

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

Status

approved