cp's OEIS Frontend

A377065 Number of 3 X n 0..2 matrices with row sums n and column sums 3 up to permutations of rows.

%I A377065 #8 Oct 15 2024 15:47:02
%S A377065 1,1,2,6,30,166,981,5937,36646,229350,1451757,9274057,59699729,
%T A377065 386798777,2520034050,16497343046,108454221206,715629888822,
%U A377065 4737625385061,31456633327905,209418369288865,1397521222483385,9346484009527370,62632803958053870,420481623373564025
%N A377065 Number of 3 X n 0..2 matrices with row sums n and column sums 3 up to permutations of rows.
%C A377065 Also, the number of 3 X n {-1,0,1} matrices with all rows and columns summing to zero up to permutations of rows.
%H A377065 Andrew Howroyd, <a href="/A377065/b377065.txt">Table of n, a(n) for n = 0..500</a>
%F A377065 a(n) = (A172634(n) - 1)/6 + 1.
%F A377065 a(n) = (5 + Sum_{i=0..n} Sum_{j=0..i} (-1)^(n-i)*binomial(n, i)*binomial(i, j)^3)/6.
%e A377065 The a(2) = 2 matrices are:
%e A377065   [1 1]  [2 0]
%e A377065   [1 1]  [0 2]
%e A377065   [1 1]  [1 1]
%e A377065 The a(3) = 6 matrices are:
%e A377065   [1 1 1]  [2 1 0]  [2 0 1]  [1 2 0]  [2 1 0]  [2 0 1]
%e A377065   [1 1 1]  [0 1 2]  [0 2 0]  [1 0 2]  [1 0 2]  [1 2 0]
%e A377065   [1 1 1]  [1 1 1]  [1 1 1]  [1 1 1]  [0 2 1]  [0 1 2]
%o A377065 (PARI) a(n)={(5+sum(i=0, n, sum(j=0, i, (-1)^(n-i)*binomial(n, i)*binomial(i, j)^3)))/6}
%Y A377065 Row n=3 of A377063.
%Y A377065 Cf. A172634, A377066, A377067.
%K A377065 nonn
%O A377065 0,3
%A A377065 _Andrew Howroyd_, Oct 15 2024