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Search: id:A028387
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| A028387 |
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Numbers of form n + (n+1)^2. |
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+0
71
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| 1, 5, 11, 19, 29, 41, 55, 71, 89, 109, 131, 155, 181, 209, 239, 271, 305, 341, 379, 419, 461, 505, 551, 599, 649, 701, 755, 811, 869, 929, 991, 1055, 1121, 1189, 1259, 1331, 1405, 1481, 1559, 1639, 1721, 1805, 1891, 1979, 2069, 2161, 2255
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Can be obtained as sum of Smarandache mirror sequence terms. a(n+1)=a(n)+2(n+1) where a(1)=1 - Felice Russo (felice.russo(AT)katamail.com)
a(n) = A105728(n+2,n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 18 2005
a(n+1) is the least k > a(n)+1 such that A000217(a(n))+A000217(k) is a square. - David Wasserman (wasserma(AT)spawar.navy.mil), Jun 30 2005
Values of Fibonacci polynomial n^2-n-1 for n=2,3,4,5,... - Artur Jasinski (grafix(AT)csl.pl), Nov 19 2006
Row sums of triangle A135223 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 23 2007
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REFERENCES
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Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.
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LINKS
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P. De Geest, World!Of Numbers
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FORMULA
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Not of form k + [ sqrt(k) ], k integer.
a(n)=sqrt( n(n+1)(n+2)(n+3) + 1 ). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 08 2001
(a(n))^2 = n(n+1)(n+2)(n+3) + 1 - Rainer Rosenthal (r.rosenthal(AT)web.de), Sep 04 2004
a(0) = 1, a(1) = 5, a(n) = (n+1)*a(n-1) - (n+2)*a(n-2) for n > 1 - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 24 2004
a(n) = A109128(n+2, 2). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Jun 20 2005
A127701 * [1, 2, 3,...] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 24 2007
a(n) = 2*T(n) - 1, where T(n) = A000217 = the triangular series. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 15 2007
a(n) = A005408(n) + A002378(n); A084990(n+1) = Sum(a(k): 0<=k<=n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 20 2007
Binomial transform of [1, 4, 2, 0, 0, 0,...] = (1, 5, 11, 19,...) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2007
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+2*n od: seq(a[n], n=1..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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MATHEMATICA
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Table[n^2 - n - 1, {n, 2, 20}] - Artur Jasinski (grafix(AT)csl.pl), Nov 19 2006
Table[Numerator[((n + 1)! - (n - 1)!)/(n!)], {n, 1, 30}] - Artur Jasinski (grafix(AT)csl.pl), Jan 09 2007
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CROSSREFS
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Complement of A028392. Third column of array A094954.
Cf. A062392.
Cf. A127701.
Cf. A000217.
Cf. A135223.
Adjacent sequences: A028384 A028385 A028386 this_sequence A028388 A028389 A028390
Sequence in context: A130828 A108151 A088059 this_sequence A110331 A106071 A073847
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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