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A357042
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The sum of the numbers of the central diamond of the multiplication table [1..k] X [1..k] for k=2*n-1.
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1
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1, 20, 117, 400, 1025, 2196, 4165, 7232, 11745, 18100, 26741, 38160, 52897, 71540, 94725, 123136, 157505, 198612, 247285, 304400, 370881, 447700, 535877, 636480, 750625, 879476, 1024245, 1186192, 1366625, 1566900, 1788421, 2032640, 2301057, 2595220, 2916725, 3267216, 3648385
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OFFSET
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1,2
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COMMENTS
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a(n) is the sum of the elements of the multiplication table, forming the maximum diamond in its center.
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LINKS
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FORMULA
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a(n) = n^2*(2*n^2 - 2*n + 1).
G.f.: x*(1 + 15*x + 27*x^2 + 5*x^3)/(1 - x)^5.
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EXAMPLE
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In the multiplication table [1..3] X [1..3]: a(2) = 2+2+4+6+6 = 20;
In the multiplication table [1..5] X [1..5]: a(3) = 3+4+3+6+6+8+9+8+12+12+15+16+15 = 117.
For n=3, the multiplication table [1..5] X [1..5] and the terms summed are
* 1 2 3 4 5
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1| 3
2| 4 6 8
3| 3 6 9 12 15
4| 8 12 16
5| 15
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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