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A226141
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Sum of the squared parts of the partitions of n into exactly two parts.
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2
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0, 2, 5, 18, 30, 64, 91, 156, 204, 310, 385, 542, 650, 868, 1015, 1304, 1496, 1866, 2109, 2570, 2870, 3432, 3795, 4468, 4900, 5694, 6201, 7126, 7714, 8780, 9455, 10672, 11440, 12818, 13685, 15234, 16206, 17936, 19019, 20940, 22140, 24262, 25585, 27918, 29370, 31924, 33511
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{i=1..floor(n/2)} (i^2 + (n-i)^2).
a(n) = ((n/2)^2) * (1 - ceiling(n/2) + floor(n/2)) + Sum_{i=1..n-1} i^2.
a(n) = n*(8*n^2 - 9*n + 4)/24 + (-1)^n*n^2/8. - Giovanni Resta, May 29 2013
G.f.: x^2*(2+3*x+7*x^2+3*x^3+x^4) / ( (1+x)^3*(x-1)^4 ). - R. J. Mathar, Jun 07 2013
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EXAMPLE
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a(5) = 30; 5 has exactly 2 partitions into two parts, (4,1) and (3,2). Squaring the parts and adding, we get: 1^2 + 2^2 + 3^2 + 4^2 = 30.
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MAPLE
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a:=n->sum(i^2 + (n-i)^2, i=1..floor(n/2)); seq((a(k), k=1..40);
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MATHEMATICA
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LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {0, 2, 5, 18, 30, 64, 91}, 50] (* Harvey P. Dale, Jul 23 2019 *)
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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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