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Search: id:A154560
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| A154560 |
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a(n) = (n+3)^2*n/2 + 1. |
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+0
2
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| 1, 9, 26, 55, 99, 161, 244, 351, 485, 649, 846, 1079, 1351, 1665, 2024, 2431, 2889, 3401, 3970, 4599, 5291, 6049, 6876, 7775, 8749, 9801, 10934, 12151, 13455, 14849, 16336, 17919, 19601, 21385, 23274, 25271, 27379, 29601, 31940, 34399, 36981
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = A058794(n)/2.
a(n) = A117560(n+2) - n - 1.
a(2*n) = A144129(n+1).
8*a(n) is the y value of a solution (x, y) to the Diophantine equation 2*x^3+12*x^2 = y^2. The corresponding x value is A152811(n+1).
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FORMULA
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G.f.: (1+5*x-4*x^2+x^3)/(1-x)^4.
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EXAMPLE
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a(5) = (5+3)^2*5/2+1 = 64*5/2+1 = 161.
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PROGRAM
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(PARI) {for(n=0, 40, print1((n+3)^2*n/2+1, ", "))}
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CROSSREFS
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Cf. A058794 (row 3 of A007754), A117560 (n*(n^2-1)/2-1), A144129 (4*n^3-3*n), A152811 (2*(n^2+2*n-2)).
Sequence in context: A075395 A085367 A081267 this_sequence A052153 A048468 A048771
Adjacent sequences: A154557 A154558 A154559 this_sequence A154561 A154562 A154563
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009
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