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Search: id:A001753
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| A001753 |
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Expansion of 1/((1+x)*(1-x)^6). |
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10
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| 1, 5, 16, 40, 86, 166, 296, 496, 791, 1211, 1792, 2576, 3612, 4956, 6672, 8832, 11517, 14817, 18832, 23672, 29458, 36322, 44408, 53872, 64883, 77623, 92288, 109088, 128248, 150008, 174624, 202368, 233529
(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 5 X 5 matrices with sum of elements equal to 4*n under action of dihedral group D_4.
a(n) = A108561(n+6,n) for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 10 2005
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FORMULA
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a(n)=sum{k=0..n, (-1)^(n-k)C(k+5, 5) }; a(n)=(4n^5+70n^4+460n^3+1400n^2+1936n+945)/960+(-1)^n/64. - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003
{a[n] == a[n - 2] + (n*(n + 1)*(n + 2)*(n - 1))/24, a[1] == 0, a[2] == 1}; (15*(-1)^n - 15*(-1)^(2*n) + 96*n - 160*(-1)^(2*n)*n + 200*n^2 - 200*(-1)^(2*n)*n^2 + 140*n^3 - 80*(-1)^(2*n)*n^3 + 40*n^4 - 10*(-1)^(2*n)*n^4 + 4*n^5)/960 - Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 14 2004
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EXAMPLE
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There are 5 symmetric nonnegative integer 5 X 5 matrices with sum of elements equal to 4 under action of D_4:
[1 0 0 0 1] [0 0 1 0 0] [0 0 0 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 1 0] [0 0 1 0 0] [0 0 0 0 0]
[0 0 0 0 0] [1 0 0 0 1] [0 0 0 0 0] [0 1 0 1 0] [0 0 4 0 0]
[0 0 0 0 0] [0 0 0 0 0] [0 1 0 1 0] [0 0 1 0 0] [0 0 0 0 0]
[1 0 0 0 1] [0 0 1 0 0] [0 0 0 0 0] [0 0 0 0 0] [0 0 0 0 0].
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CROSSREFS
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Cf. A000217, A002620, A038163, A054343, A008804.
Sequence in context: A027085 A099452 A006007 this_sequence A073459 A081997 A078449
Adjacent sequences: A001750 A001751 A001752 this_sequence A001754 A001755 A001756
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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Comment and example from Vladeta Jovovic (vladeta(AT)Eunet.yu), May 14 2000
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