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Search: id:A118058
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| A118058 |
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a(n)=49n^2-28n-20; a(n)+(a(n)+1)+...+(a(n)+49n+34)=(a(n)+49n+35)+...+a(n+1)-1; a(n+1)-1=a(n)+98n+20. |
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+0
3
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| 1, 120, 337, 652, 1065, 1576, 2185, 2892, 3697, 4600, 5601, 6700, 7897, 9192, 10585, 12076, 13665, 15352, 17137, 19020, 21001, 23080, 25257, 27532, 29905, 32376, 34945, 37612, 40377, 43240, 46201, 49260, 52417, 55672, 59025, 62476, 66025
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In general, all sequences of equations which contain every positive integer in order exactly once (a pair wise equal summed, ordered partition of the positive integers) may be defined as follows: For all k, let x(k)=A001652(k) and z(k)=A001653(k). Then if we define a(n) to be (x(k)+z(k))n^2-(z(k)-1)n-x(k), the following equation is true: a(n)+(a(n)+1)+...+(a(n)+(x(k)+z(k))n+(2x(k)+z(k)-1)/2)=(a(n)+ (x(k)+z(k))n+(2x(k)+z(k)+1)/2)+...+(a(n)+2(x(k)+z(k))n+x(k)); a(n)+2(x(k)+z(k))n+x(k))=a(n+1)-1; e.g., in this sequence, x(2)=A001652(2) and z(2)=A001653(2)=29; cf. A000290,A118057,A118059-A118061.
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FORMULA
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a(n)+(a(n)+1)+...+(a(n)+98n+34)=7(7n-2)(7n+5)(14n+3)/2; e.g., 337+338+...+518=77805=7*19*26*45/2.
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EXAMPLE
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a(3)=49*3^2-28*3-20=337, a(4)=49*4^2-28*4-20=652 and 337+338+...+518=519+...+651.
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CROSSREFS
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Sequence in context: A090391 A098114 A135805 this_sequence A052768 A061218 A052778
Adjacent sequences: A118055 A118056 A118057 this_sequence A118059 A118060 A118061
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KEYWORD
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nonn
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AUTHOR
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Charlie Marion (charliemath(AT)optonline.net), Apr 26 2006
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EXTENSIONS
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Corrected by Franklin T. Adams-Watters and T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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