OFFSET
2,2
COMMENTS
From Gus Wiseman, Jan 22 2019: (Start)
Also the number of non-isomorphic multiset partitions of weight n with exactly 2 distinct vertices and exactly 2 (not necessarily distinct) edges. For example, non-isomorphic representatives of the a(2) = 1 through a(5) = 9 multiset partitions are:
{{1}{2}} {{1}{22}} {{1}{122}} {{11}{122}}
{{2}{12}} {{11}{22}} {{1}{1222}}
{{12}{12}} {{11}{222}}
{{1}{222}} {{12}{122}}
{{12}{22}} {{1}{2222}}
{{2}{122}} {{12}{222}}
{{2}{1122}}
{{2}{1222}}
{{22}{122}}
(End)
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
G.f.: -x^2*(x^3-x^2-1) / ((x^2-1)^2*(x-1)^2).
From Colin Barker, Jan 16 2017: (Start)
a(n) = (6 - 6*(-1)^n + (9*(-1)^n-17)*n + 12*n^2 + 2*n^3) / 48.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>7.
(End)
EXAMPLE
There are 9 nonnegative integer 2 X 2 matrices with no zero rows or columns and with sum of elements equal to 5, up to row and column permutation:
[0 1] [0 1] [0 1] [0 1] [0 2] [0 2] [0 2] [0 3] [1 1]
[1 3] [2 2] [3 1] [4 0] [1 2] [2 1] [3 0] [1 1] [1 2].
MAPLE
gf := -x^2*(x^3-x^2-1)/((x^2-1)^2*(x-1)^2): s := series(gf, x, 101): for i from 2 to 100 do printf(`%d, `, coeff(s, x, i)) od:
PROG
(PARI) Vec(-x^2*(x^3-x^2-1) / ((x^2-1)^2*(x-1)^2) + O(x^60)) \\ Colin Barker, Jan 16 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, May 28 2000
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved