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A275591
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a(n) = n^2 + 9*n + 1.
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0
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1, 11, 23, 37, 53, 71, 91, 113, 137, 163, 191, 221, 253, 287, 323, 361, 401, 443, 487, 533, 581, 631, 683, 737, 793, 851, 911, 973, 1037, 1103, 1171, 1241, 1313, 1387, 1463, 1541, 1621, 1703, 1787, 1873, 1961, 2051, 2143, 2237, 2333, 2431, 2531, 2633, 2737
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OFFSET
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0,2
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COMMENTS
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Also, nonnegative integers m such that 4*m + 77 is a square. The negative values of m are -7, -13, -17, -19.
The product of two consecutive terms belongs to the sequence. In fact: a(k)*a(k+1) = a(k*(k+1)+9*k+1).
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LINKS
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FORMULA
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O.g.f.: (1 + 8*x - 7*x^2)/(1 - x)^3. - Colin Barker, Aug 03 2016
E.g.f.: (1 + 10*x + x^2)*exp(x).
a(n) = a(-n-9) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Colin Barker, Aug 03 2016
a(n) + a(-n) = (n-1)^2 + (n+1)^2.
Sum_{i>=0} 1/a(i) = 9736/29393 + tan(sqrt(77)*Pi/2)*Pi/sqrt(77) = 1.301517...
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MATHEMATICA
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PROG
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(PARI) Vec((1+8*x-7*x^2)/(1-x)^3 + O(x^100)) \\ Colin Barker, Aug 04 2016
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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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EXTENSIONS
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STATUS
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approved
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