A070307 Number of n X n matrices with nonnegative integer entries such that every row sum equals 3.

1, 16, 1000, 160000, 52521875, 30840979456, 29509034655744, 42998169600000000, 90647430472564453125, 265599227914240000000000, 1047192117300356121695451136, 5410240907043328777415185924096, 35821862005173382840059779052734375, 298285661929377847941529600000000000000

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..160

Crossrefs

Cf. A061718, A000292.

Programs

Mathematica

Table[ Binomial[n + 2, 3]^n, {n, 1, 14}]

PARI

a(n) = binomial(n+2, 3)^n; \\ Michel Marcus, Mar 10 2017

Python

import math
f=math.factorial
def C(n, r): return f(n)/ f(r)/ f(n-r)
def A070307(n): return C(n + 2, 3)**n # Indranil Ghosh, Mar 10 2017

Formula

a(n) = C(n+2, 3)^n = A000292(n)^n.

a(n) ~ 6^(-n)*exp(3-5/(2*n))*n^(3*n). - Stefano Spezia, Jun 13 2025

Extensions

More terms from Robert G. Wilson v, May 10 2002

More terms from Michel Marcus, Mar 10 2017