A162254 a(n) = n*(2*n^2 + 5*n + 1)/2.

4, 19, 51, 106, 190, 309, 469, 676, 936, 1255, 1639, 2094, 2626, 3241, 3945, 4744, 5644, 6651, 7771, 9010, 10374, 11869, 13501, 15276, 17200, 19279, 21519, 23926, 26506, 29265, 32209, 35344, 38676, 42211, 45955, 49914, 54094, 58501, 63141

Offset: 1

Author

Vincenzo Librandi, Jun 29 2009

Keywords

• nonn
• easy

Comments

Row sums from A083487.

Row 2 of the convolution array A213831. - Clark Kimberling, Jul 04 2012

Number of CNF statements for checking whether a 3-colored n X n grid has no monochromatic L. See Mammel et al. - Michel Marcus, Feb 10 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Isaac Mammel, William Smith, and Carl Yerger, Ramsey Theory on the Integer Grid: The "L" Problem, arXiv:2502.05162 [math.CO], 2025. See p. 14.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

LinearRecurrence[{4,-6,4,-1}, {4, 19, 51, 106}, 50] (* or *) CoefficientList[Series[(4+3*x-x^2)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Mar 04 2012 *)

PARI

a(n)=n*(5*n+1)/2+n^3 \\ Charles R Greathouse IV, Jan 11 2012

Formula

From Vincenzo Librandi, Mar 04 2012: (Start)

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

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

Extensions

New name from Charles R Greathouse IV, Jan 11 2012