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A010000
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a(0) = 1, a(n) = n^2 + 2 for n>0.
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15
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1, 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Least k such that A070864(k) = 2n-1. - Robert G. Wilson v (rgwv(AT)rgwv.com) and Benoit Cloitre (benoit7848c(AT)orange.fr), May 20 2002
With an offset of 3, beginning with 6 (deleting first two terms) n*(n+a(n)) + 1 is a cube = (n+1)^3: 1(1+6) +1 = 8, 2(2+11) +1 = 27 etc. - Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), May 03 2003
For n>=2, a(n) is the maximum element in the continued fraction for sum(k>=1,1/n^(2^k)) (for n=2 see A006464) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2007
Equals binomial transform of [1, 2, 1, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
Euler transform of length 6 sequence [ 3, 0, 1, 0, 0, -1]. - Michael Somos Aug 11 2009
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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
| a(n) = A000217(n-2)+A000217(n+1) for n>0. - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003
G.f.: (1 + x^3) / (1 - x)^3. a(-n) = a(n). - Michael Somos Aug 11 2009
E.g.f.: (x*(x+1)+2)*e^x-1. - Gopinath A. R., Feb 14 2012
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EXAMPLE
| 1 + 3*x + 6*x^2 + 11*x^3 + 18*x^4 + 27*x^5 + 38*x^6 + 51*x^7 + 66*x^8 + ...
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MATHEMATICA
| a[1] = a[2] = 1; a[n_] := a[n] = 2 + a[n - a[n - 1]]; b = Table[0, {100}]; Do[c = (a[n] + 1)/2; If[c < 101 && b[[c]] == 0, b[[c]] = n], {n, 1, 10^4}]; b
Join[{1}, Range[50]^2 + 2] (* Bruno Berselli, Feb 08 2012 *)
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PROG
| (PARI) {a(n) = n^2 + 2 - (n==0)} /* Michael Somos Aug 11 2009 */
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CROSSREFS
| Cf. A070864. Apart from initial terms, same as A059100.
Cf. A206399.
Sequence in context: A025210 A140126 A140235 * A183199 A172046 A014125
Adjacent sequences: A009997 A009998 A009999 * A010001 A010002 A010003
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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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