|
Search: id:A054975
|
|
|
| A054975 |
|
Number of nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to n, up to row and column permutation. |
|
+0
3
|
|
| 1, 3, 13, 38, 97, 217, 453, 868, 1585, 2756, 4606, 7440, 11679, 17849, 26674, 39060, 56144, 79387, 110575, 151904, 206063, 276332, 366561, 481484, 626586, 808431, 1034636, 1314242, 1657500, 2076601, 2585262, 3199504, 3937370, 4819788
(list; graph; listen)
|
|
|
OFFSET
|
3,2
|
|
|
FORMULA
|
G.f.: x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x + 1)^3*(x - 1)^5).
|
|
EXAMPLE
|
There are 3 nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to 4, up to row and column permutation:
[0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 1 0] [0 1 0]
[1 1 0] [1 0 1] [2 0 0].
|
|
MAPLE
|
gf := x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x+1)^3*(x - 1)^5): s := series(gf, x, 101): for i from 3 to 100 do printf(`%d, `, coeff(s, x, i)) od:
|
|
CROSSREFS
|
Cf. A052365.
Sequence in context: A019007 A147554 A076800 this_sequence A072790 A166911 A103657
Adjacent sequences: A054972 A054973 A054974 this_sequence A054976 A054977 A054978
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Vladeta Jovovic (vladeta(AT)eunet.rs), May 28 2000
|
|
EXTENSIONS
|
More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 29 2000
|
|
|
Search completed in 0.002 seconds
|
