A334707 Number of non-collinear triples in a 5 X n rectangular grid.

0, 100, 412, 1056, 2148, 3820, 6176, 9352, 13456, 18612, 24940, 32568, 41596, 52164, 64384, 78376, 94256, 112156, 132180, 154464, 179116, 206260, 236016, 268512, 303848, 342164, 383572, 428192, 476140, 527548, 582520, 641192, 703672, 770084, 840548, 915192, 994116

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,-1,1,-1,-1,1,-1,2,-1).

Crossrefs

A row of A334705.

Formula

From Stefano Spezia, Jun 20 2020: (Start)

G.f.: 4*x*(25 + 53*x + 83*x^2 + 87*x^3 + 67*x^4 + 35*x^5 + 10*x^6)/((1 - x)^4*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) - a(n-5) + a(n-6) - a(n-7) + 2*a(n-8) - a(n-9) for n > 9. (End)

Extensions

Terms a(6) and beyond from Giovanni Resta, Jun 20 2020