A135859 Row sums of triangle A135858.

1, 4, 13, 34, 73, 136, 229, 358, 529, 748, 1021, 1354, 1753, 2224, 2773, 3406, 4129, 4948, 5869, 6898, 8041, 9304, 10693, 12214, 13873, 15676, 17629, 19738, 22009, 24448, 27061, 29854, 32833, 36004, 39373, 42946, 46729, 50728, 54949

Offset: 1

Author

Gary W. Adamson, Dec 01 2007

Keywords

• nonn
• easy

Comments

Number of binary 3 X (n-1) matrices such that each row and column has at most one 1. - Dmitry Kamenetsky, Jan 20 2018

Examples

			a(3) = 13 = sum of row 3 terms of triangle A135858: (7, + 5 + 1).
a(4) = 34 = (1, 3, 3, 1) dot (1, 3, 6, 6) = (1 + 9 + 18 + 6).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• R. J. Mathar, The number of binary matrices..., Table 1 column 3.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A135858.

Programs

GAP

List([1..10^4], n-> 5*n - 2 + n^3 - 3*n^2); # Muniru A Asiru, Jan 24 2018

Magma

I:=[1, 4, 13, 34]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012

Maple

seq(5*n - 2 + n^3 - 3*n^2, n=1..10^2); # Muniru A Asiru, Jan 24 2018

Mathematica

CoefficientList[Series[(1+3*x^2+2*x^3)/(x-1)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 29 2012 *)

SageMath

[n^3 -3*n^2 +5*n -2 for n in (1..50)] # G. C. Greubel, Aug 11 2022

Formula

Row sums of triangle A135858. Binomial transform of [1, 3, 6, 6, 0, 0, 0, ...].

G.f.: x*(1+3*x^2+2*x^3) / (1-x)^4. - R. J. Mathar, Apr 04 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012

a(n) = n^3 - 3*n^2 + 5*n - 2. - R. J. Mathar, Oct 20 2017

E.g.f.: 2 - (2 - 3*x - x^3)*exp(x). - G. C. Greubel, Aug 11 2022