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

1,2

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).

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)

a(n) = 20*n^3 - 83/6*n^2 + O(1). - Charles R Greathouse IV, May 31 2026

Prog

(PARI) a(n)=(120*n^3-83*n^2+[0, -37, -28, -21, -16, -37, -12, -37, -16, -21, -28, -37][n%12+1])/6 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

A row of A334705.

Sequence in context: A250853 A017270 A105089 * A017510 A290654 A017642

Adjacent sequences: A334704 A334705 A334706 * A334708 A334709 A334710

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Jun 13 2020

Extensions

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

Status

approved