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Search: id:A135405
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| A135405 |
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Sequence where the sum of each pair of consecutive elements is a square. This covers squares of all consecutively increasing integers with the exception of 2. |
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+0
1
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| 0, 1, 8, 8, 17, 19, 30, 34, 47, 53, 68, 76, 93, 103, 122, 134, 155, 169, 192, 208, 233, 251, 278, 298, 327, 349, 380, 404, 437, 463, 498, 526, 563, 593, 632, 664, 705, 739, 782, 818, 863, 901, 948, 988, 1037, 1079, 1130, 1174, 1227, 1273, 1328, 1376, 1433, 1483
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n)=(n+2)*(n+1)/2+2*(-1)^n
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FORMULA
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O.g.f.: -x*(1+6*x-8*x^2+3*x^3)/((-1+x)^3*(1+x)) = -3-1/(-1+x)^3+2/(1+x). a(n)= A000217(n+1)+2*(-1)^n if n>0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2007
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EXAMPLE
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a(1)=1 because 0 + 1 = 1^2
a(2)=8 because 1 + 8 = 9 = 3^2
a(3)=8 because 8 + 8 =16 = 4^2
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MATHEMATICA
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a=1; lst={0, a}; Do[a=n^2-a; AppendTo[lst, a], {n, 3, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 17 2008]
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CROSSREFS
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Sequence in context: A112439 A022091 A145909 this_sequence A006784 A061156 A109049
Adjacent sequences: A135402 A135403 A135404 this_sequence A135406 A135407 A135408
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KEYWORD
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nonn
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 11 2007, Apr 02 2008
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EXTENSIONS
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More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 17 2008
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