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A010009
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a(0) = 1, a(n) = 19*n^2 + 2 for n>0.
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1
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1, 21, 78, 173, 306, 477, 686, 933, 1218, 1541, 1902, 2301, 2738, 3213, 3726, 4277, 4866, 5493, 6158, 6861, 7602, 8381, 9198, 10053, 10946, 11877, 12846, 13853, 14898, 15981, 17102, 18261, 19458, 20693, 21966, 23277, 24626, 26013, 27438, 28901, 30402, 31941
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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=1, s=3. After 1, all terms are in A000408. - Bruno Berselli, Feb 06 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+17*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*19+2)*e^x-1. - Gopinath A. R., Feb 14 2012
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MATHEMATICA
| Join[{1}, 19 Range[41]^2 + 2] (* From Harvey P. Dale, Feb 07 2011 *)
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CROSSREFS
| Cf. A206399.
Sequence in context: A182754 A045559 A144314 * A172082 A068085 A135945
Adjacent sequences: A010006 A010007 A010008 * A010010 A010011 A010012
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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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