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A054974 Number of nonnegative integer 2 X 2 matrices with no zero rows or columns and with sum of elements equal to n, up to row and column permutation. 7
1, 2, 6, 9, 17, 23, 36, 46, 65, 80, 106, 127, 161, 189, 232, 268, 321, 366, 430, 485, 561, 627, 716, 794, 897, 988, 1106, 1211, 1345, 1465, 1616, 1752, 1921, 2074, 2262, 2433, 2641, 2831, 3060, 3270, 3521, 3752, 4026, 4279, 4577, 4853, 5176, 5476, 5825, 6150 (list; graph; refs; listen; history; text; internal format)
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

Cf. A007716, A052847, A053307, A323654, A323655, A323656.

Sequence in context: A280228 A254057 A257083 * A072481 A032471 A156222

Adjacent sequences:  A054971 A054972 A054973 * A054975 A054976 A054977

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, May 28 2000

EXTENSIONS

More terms from James A. Sellers, May 29 2000

STATUS

approved

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Last modified April 21 08:51 EDT 2019. Contains 322328 sequences. (Running on oeis4.)