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Search: id:A010000
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| A010000 |
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a(0)=1, a(n)=n^2 + 2, n >= 1. |
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+0
12
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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; listen)
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OFFSET
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0,2
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COMMENT
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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
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FORMULA
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a(n)=A000217(n-2)+A000217(n+1) for n>0. - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003
Equals binomial transform of [1, 2, 1, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
Expansion of (1 - x^6) / ((1 - x)^3 * (1 - x^3)) in powrs of x. - Michael Somos Aug 11 2009
Euler transform of length 6 sequence [ 3, 0, 1, 0, 0, -1]. - Michael Somos Aug 11 2009
G.f.: (1 + x^3) / (1 - x)^3. a(-n) = a(n). - Michael Somos Aug 11 2009
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EXAMPLE
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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
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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
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PROGRAM
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(PARI) {a(n) = n^2 + 2 - (n==0)} /* Michael Somos Aug 11 2009 */
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CROSSREFS
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Cf. A070864. Apart from initial terms, same as A059100.
Sequence in context: A025210 A140126 A140235 this_sequence A014125 A147456 A011849
Adjacent sequences: A009997 A009998 A009999 this_sequence A010001 A010002 A010003
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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