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A146302
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a(n) = (8*n+5)*(8*n+9).
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1
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45, 221, 525, 957, 1517, 2205, 3021, 3965, 5037, 6237, 7565, 9021, 10605, 12317, 14157, 16125, 18221, 20445, 22797, 25277, 27885, 30621, 33485, 36477, 39597, 42845, 46221, 49725, 53357, 57117, 61005, 65021, 69165, 73437, 77837, 82365
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OFFSET
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0,1
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COMMENTS
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f(y) = y^4*(1 + y^4) = y^4 - y^8 + y^12 - y^16 + y^20 - y^24 + ...
Integral_{y} f(y) dy = y^5/5 - y^9/9 + y^13/13 - y^17/17 + y^21/21 - y^25/25 + ...
Integral_{y=0..1} f(y) dy = 1/5 - 1/9 + 1/13 - 1/17 + 1/21 - 1/25 + ...
= (9 - 5)/(5*9) + (17 - 13)/(13*17) + (25 - 21)/(21*25) + ...
= 4/(5*9) + 4/(13*17) + 4/(21*25) + ...
Integral_{y=0..1} f(y) dy = Sum_{m>=0} 4/((8*m+5)*(8*m+9))
= -(1/8)*sqrt(2)*Pi + 1 - (1/4)*sqrt(2)*log(1+sqrt(2))
= 0.13302701266008896241... (End)
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LINKS
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FORMULA
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G.f: (45 + 86*x - 3*x^2)/(1-x)^3.
E.g.f.: (45 + 176*x + 64*x^2)*exp(x).
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MAPLE
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MATHEMATICA
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Table[(8n+5)(8n+9), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {45, 221, 525}, 40] (* Harvey P. Dale, Oct 10 2015 *)
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PROG
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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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