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A262000
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a(n) = n^2*(7*n - 5)/2.
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6
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0, 1, 18, 72, 184, 375, 666, 1078, 1632, 2349, 3250, 4356, 5688, 7267, 9114, 11250, 13696, 16473, 19602, 23104, 27000, 31311, 36058, 41262, 46944, 53125, 59826, 67068, 74872, 83259, 92250, 101866, 112128, 123057, 134674, 147000, 160056, 173863, 188442, 203814, 220000
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OFFSET
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0,3
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COMMENTS
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Also, structured enneagonal prism numbers.
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LINKS
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FORMULA
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G.f.: x*(1 + 14*x + 6*x^2)/(1 - x)^4.
a(n) = Sum_{i=0..n-1} n*(7*i+1) for n>0, a(0)=0.
Sum_{i>0} 1/a(i) = 1.082675669875907610300284768825... = (42*(log(14) + 2*(cos(Pi/7)*log(cos(3*Pi/14)) + log(sin(Pi/7))*sin(Pi/14) - log(cos(Pi/14)) * sin(3*Pi/14))) + 21*Pi*tan(3*Pi/14))/75 - Pi^2/15. - Vaclav Kotesovec, Oct 04 2016
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EXAMPLE
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For n=8, a(8) = 8*(7*0+1)+8*(7*1+1)+8*(7*2+1)+8*(7*3+1)+8*(7*4+1)+8*(7*5+1)+8*(7*6+1)+8*(7*7+1) = 1632.
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MATHEMATICA
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Table[n^2 (7 n - 5)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 18, 72}, 50] (* Harvey P. Dale, Oct 04 2016 *)
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PROG
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(PARI) vector(40, n, n--; n^2*(7*n-5)/2)
(Sage) [n^2*(7*n-5)/2 for n in (0..40)]
(Magma) [n^2*(7*n-5)/2: n in [0..40]];
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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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