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A213801
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Number of 3 X 3 0..n symmetric arrays with all rows summing to floor(n*3/2).
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1
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4, 13, 29, 57, 96, 153, 226, 323, 440, 587, 759, 967, 1204, 1483, 1796, 2157, 2556, 3009, 3505, 4061, 4664, 5333, 6054, 6847, 7696, 8623, 9611, 10683, 11820, 13047, 14344, 15737, 17204, 18773, 20421, 22177, 24016, 25969, 28010, 30171, 32424, 34803, 37279
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OFFSET
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1,1
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COMMENTS
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Sequence is difference between numbers of triangles, regardless of size, in A064412 (a family of ((3*n^2+3*n+2)/2-iamonds, see also illustration of initial terms there) and a quantity A077043 of triangles of dimension 1. - Luce ETIENNE, Aug 23 2014
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) -2*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-7) -a(n-8).
Empirical: G.f. -x*(-4-5*x-3*x^2-7*x^3-x^5-2*x^6+x^7) / ( (x^2+1)*(1+x)^2*(x-1)^4 ). - R. J. Mathar, Jul 04 2012
a(n) = (14*n^3+42*n^2+53*n+25+3*(n+1)*(-1)^n+2*((-1)^((2*n+1-(-1)^n)/4)-(-1)^((6*n+5-(-1)^n)/4)))/32. - Luce ETIENNE, Aug 23 2014
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EXAMPLE
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Some solutions for n=4:
..1..3..2....2..4..0....0..4..2....1..2..3....1..1..4....4..0..2....2..2..2
..3..1..2....4..0..2....4..0..2....2..2..2....1..3..2....0..2..4....2..2..2
..2..2..2....0..2..4....2..2..2....3..2..1....4..2..0....2..4..0....2..2..2
a(2)=5-1=4, a(3)=14-1=13, a(210)=4118206-8269=4109937. - Luce ETIENNE, Aug 23 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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