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Search: id:A038163
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| A038163 |
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G.f.: 1/((1-x)*(1-x^2))^3. |
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+0
12
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| 1, 3, 9, 19, 39, 69, 119, 189, 294, 434, 630, 882, 1218, 1638, 2178, 2838, 3663, 4653, 5863, 7293, 9009, 11011, 13377, 16107, 19292, 22932, 27132, 31892, 37332, 43452, 50388, 58140, 66861, 76551, 87381, 99351, 112651, 127281
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of symmetric nonnegative integer 6 X 6 matrices with sum of elements equal to 4*n, under action of dihedral group D_4 - Vladeta Jovovic (vladeta(AT)eunet.rs), May 14 2000
Equals the triangular sequence convolved with the aerated triangular sequence, [1, 0, 3, 0, 10,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 11 2009]
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 26 2009: (Start)
Number of partitions of n (n>=1) into 1s and 2s if there are three kinds of 1s and three kinds of 2s. Example: a(2)=9 because we have 11, 11', 11", 1'1', 1'1", 1"1", 2, 2', and 2".
(End)
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FORMULA
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a(2*k) = (4*k + 5)*binomial(k + 4, 4)/5 = A034263(k); a(2*k + 1) = binomial(k + 4, 4)*(15 + 4*k)/5 = A059599(k), k >= 0.
a(n) = 1/3840*(4*n^5+90*n^4+760*n^3+2970*n^2+5266*n+3285+(-1)^n*(30*n^2+270*n+555)). Recurrence: a(n) = 3*a(n-1)-8*a(n-3)+6*a(n-4)+6*a(n-5)-8*a(n-6)+3*a(n-8)-a(n-9). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 24 2002
a(n+1)-a(n) = A096338(n+2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 04 2008]
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MAPLE
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G := 1/((1-x)^3*(1-x^2)^3): Gser := series(G, x = 0, 42): seq(coeff(Gser, x, n), n = 0 .. 37); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 26 2009]
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CROSSREFS
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Cf. A008619, A006918, A001753.
Cf. A096338.
Sequence in context: A005994 A080010 A135117 this_sequence A146819 A147213 A146441
Adjacent sequences: A038160 A038161 A038162 this_sequence A038164 A038165 A038166
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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