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Number of n X n matrices with nonnegative integer entries such that every row sum equals 3.
2

%I #8 Mar 10 2017 03:00:47

%S 1,16,1000,160000,52521875,30840979456,29509034655744,

%T 42998169600000000,90647430472564453125,265599227914240000000000,

%U 1047192117300356121695451136,5410240907043328777415185924096,35821862005173382840059779052734375,298285661929377847941529600000000000000

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

%H Indranil Ghosh, <a href="/A070307/b070307.txt">Table of n, a(n) for n = 1..160</a>

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

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

%o (PARI) a(n) = binomial(n+2, 3)^n; \\ _Michel Marcus_, Mar 10 2017

%o (Python)

%o import math

%o f=math.factorial

%o def C(n, r): return f(n)/ f(r)/ f(n-r)

%o def A070307(n): return C(n + 2, 3)**n # _Indranil Ghosh_, Mar 10 2017

%Y Cf. A061718, A000292.

%K nonn

%O 1,2

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

%E More terms from _Robert G. Wilson v_, May 10 2002

%E More terms from _Michel Marcus_, Mar 10 2017