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A177059
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a(n) = 25*n^2 + 25*n + 6.
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7
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6, 56, 156, 306, 506, 756, 1056, 1406, 1806, 2256, 2756, 3306, 3906, 4556, 5256, 6006, 6806, 7656, 8556, 9506, 10506, 11556, 12656, 13806, 15006, 16256, 17556, 18906, 20306, 21756, 23256, 24806, 26406, 28056, 29756, 31506, 33306, 35156, 37056
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = (5n + 2)*(5n + 3).
a(n) = 50*n + a(n-1) with a(0)=6.
Sum_{n>=0} 1/a(n) = sqrt(1 - 2/sqrt(5))*Pi/5.
Sum_{n>=0} (-1)^n/a(n) = 2*log(phi)/sqrt(5) - 2*log(2)/5, where phi is the golden ratio (A001622).
Product_{n>=0} (1 - 1/a(n)) = 2*sqrt(2/(5+sqrt(5))) * cos(Pi/(2*sqrt(5))).
Product_{n>=0} (1 + 1/a(n)) = sqrt(2 - 2/sqrt(5)) * cosh(sqrt(3)*Pi/10).
Product_{n>=0} (1 - 2/a(n)) = 1/phi. (End)
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MATHEMATICA
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PROG
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(Magma) I:=[6, 56, 156]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012
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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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