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A054343 Number of nonnegative integer 3 X 3 matrices with sum of elements equal to n, under action of dihedral group of the square D_4. 3
1, 3, 11, 31, 84, 198, 440, 904, 1766, 3266, 5802, 9906, 16384, 26284, 41104, 62752, 93831, 137589, 198309, 281249, 393148, 542154, 738480, 994320, 1324668, 1747220, 2283396, 2958228, 3801600, 4848120, 6138624, 7720032, 9647133, 11982423, 14798223, 18176499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-8,0,16,-24,16,8,-34,34,-8,-16,24,-16,0,8,-5,1).

FORMULA

G.f.: (2*x^6+2*x^5+x^4+4*x^2-2*x+1)/((1-x^4)^2*(1-x^2)^2*(1-x)^5).

a(n) = 5*a(n-1) - 8*a(n-2) + 16*a(n-4) - 24*a(n-5) + 16*a(n-6) + 8*a(n-7) - 34*a(n-8) + 34*a(n-9) - 8*a(n-10) - 16*a(n-11) + 24*a(n-12) - 16*a(n-13) + 8*a(n-15) - 5*a(n-16) + a(n-17) for n>16. - Colin Barker, Apr 26 2019

EXAMPLE

There are 11 nonisomorphic nonnegative integer 3 X 3 matrices with sum of elements equal to 2, under action of D_4:

[0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 1] [0 0 0] [0 0 0] [0 0 0]

[0 0 0] [0 0 0] [0 0 1] [0 0 1] [0 1 0] [0 1 0] [1 0 1] [0 0 0] [0 0 0] [0 0 0] [0 2 0]

[0 1 1] [1 0 1] [0 1 0] [1 0 0] [0 0 1] [0 1 0] [0 0 0] [1 0 0] [0 0 2] [0 2 0] [0 0 0].

PROG

(PARI) Vec((2*x^6+2*x^5+x^4+4*x^2-2*x+1)/((1-x^4)^2*(1-x^2)^2*(1-x)^5) + O(x^40)) \\ Colin Barker, Apr 26 2019

CROSSREFS

Cf. A005232, A052365.

Sequence in context: A236752 A034543 A268800 * A320238 A108898 A291887

Adjacent sequences:  A054340 A054341 A054342 * A054344 A054345 A054346

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, May 05 2000

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)