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A010008
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a(0) = 1, a(n) = 18*n^2 + 2 for n>0.
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2
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1, 20, 74, 164, 290, 452, 650, 884, 1154, 1460, 1802, 2180, 2594, 3044, 3530, 4052, 4610, 5204, 5834, 6500, 7202, 7940, 8714, 9524, 10370, 11252, 12170, 13124, 14114, 15140, 16202, 17300, 18434, 19604, 20810, 22052, 23330, 24644, 25994, 27380, 28802, 30260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The identity (18*n^2+2)^2-(9*n^2+2)*(6*n)^2=4 can be written as a(n+1)^2-A010002(n+1)*A008588(n+1)^2=4. - Vincenzo Librandi, Feb 07 2012
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LINKS
| Bruno Berselli, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: (1+x)*(1+16*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
a(n) = (3*n-1)^2+(3*n+1)^2 = (n-1)^2+(n+1)^2+(4*n)^2 for n>0. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*18+2)*e^x-1. - Gopinath A. R., Feb 14 2012
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MATHEMATICA
| Join[{1}, 18 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
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CROSSREFS
| After 20, all terms are in A000408.
Cf. A206399.
Sequence in context: A139241 A139232 A002292 * A000529 A005565 A066126
Adjacent sequences: A010005 A010006 A010007 * A010009 A010010 A010011
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KEYWORD
| nonn,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Bruno Berselli, Feb 06 2012
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