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A010003
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a(0) = 1, a(n) = 11*n^2 + 2 for n>0.
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1
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1, 13, 46, 101, 178, 277, 398, 541, 706, 893, 1102, 1333, 1586, 1861, 2158, 2477, 2818, 3181, 3566, 3973, 4402, 4853, 5326, 5821, 6338, 6877, 7438, 8021, 8626, 9253, 9902, 10573, 11266, 11981, 12718, 13477, 14258, 15061, 15886, 16733, 17602, 18493, 19406
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OFFSET
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0,2
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COMMENTS
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Apart from the first term, numbers of the form (r^2+2*s^2)*n^2+2 = (r*n)^2+(s*n-1)^2+(s*n+1)^2: in this case is r=3, s=1. After 13, all terms are in A000408. - Bruno Berselli, Feb 06 2012
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LINKS
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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
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G.f.: (1+x)*(1+9*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*11+2)*e^x-1. - Gopinath A. R., Feb 14 2012
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MATHEMATICA
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Join[{1}, 11 Range[41]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
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PROG
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(PARI) A010003(n)=11*n^2+2-!n \\ - M. F. Hasler, Feb 14 2012
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CROSSREFS
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Cf. A206399.
Sequence in context: A141549 A121964 A147208 * A007587 A219905 A034462
Adjacent sequences: A010000 A010001 A010002 * A010004 A010005 A010006
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Bruno Berselli, Feb 06 2012
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STATUS
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approved
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