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A135859 Row sums of triangle A135858. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 29 06:53 EST 2022. Contains 358422 sequences. (Running on oeis4.)