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

1,2

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

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).

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

Example

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).

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 *)

Prog

(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
(GAP) List([1..10^4], n-> 5*n - 2 + n^3 - 3*n^2); # Muniru A Asiru, Jan 24 2018
(SageMath) [n^3 -3*n^2 +5*n -2 for n in (1..50)] # G. C. Greubel, Aug 11 2022

Crossrefs

Cf. A135858.

Sequence in context: A227122 A176361 A322599 * A161531 A101946 A029860

Adjacent sequences: A135856 A135857 A135858 * A135860 A135861 A135862

Keyword

nonn,easy

Author

Gary W. Adamson, Dec 01 2007

Status

approved