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A126719
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-n^2 + 9n + 23.
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6
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23, 31, 37, 41, 43, 43, 41, 37, 31, 23, 13, 1, -13, -29, -47, -67, -89, -113, -139, -167, -197, -229, -263, -299, -337, -377, -419, -463, -509, -557, -607, -659, -713, -769, -827, -887, -949, -1013, -1079, -1147, -1217, -1289, -1363, -1439, -1517, -1597, -1679, -1763, -1849, -1937, -2027, -2119, -2213
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Derivation is similar to that of A126665, which see for further information.
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LINKS
| Michael M. Ross, Natural Numbers
Robert Sacks Number Spiral: Method of Common Differences.
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| a(0)=23, a(1)=31, a(2)=37, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, Oct 19 2011]
G.f.: ((38-13*x)*x-23)/(x-1)^3 [From Harvey P. Dale, Oct 19 2011]
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EXAMPLE
| -1*8^2 + 9*8 + 23 = 31
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MATHEMATICA
| Table[-n^2+9n+23, {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {23, 31, 37}, 60] (* From Harvey P. Dale, Oct 19 2011 *)
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PROG
| QTest: Quadratic equation derivation and prime number generation. Vortex: View and analyze the Sacks Number Spiral.
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CROSSREFS
| Sequence in context: A036267 A107934 A155107 * A110677 A169640 A026051
Adjacent sequences: A126716 A126717 A126718 * A126720 A126721 A126722
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KEYWORD
| sign
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AUTHOR
| Michael M. Ross (michaelmross(AT)comcast.net), Mar 13 2007
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