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Search: id:A153642
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| 36, 72, 116, 168, 228, 296, 372, 456, 548, 648, 756, 872, 996, 1128, 1268, 1416, 1572, 1736, 1908, 2088, 2276, 2472, 2676, 2888, 3108, 3336, 3572, 3816, 4068, 4328, 4596, 4872, 5156, 5448, 5748, 6056, 6372, 6696, 7028, 7368, 7716, 8072, 8436, 8808, 9188
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OFFSET
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1,1
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COMMENT
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2*(fifth subdiagonal of triangle A144562).
Sequence gives values x of solutions (x, y) to the Diophantine equation x^3+28*x^2 = y^2. For a more comprehensive list of solutions see A155135.
a(n) = A155135(2n+8) = A155136(2n+7).
a(n) = 4*A028881(n+3).
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FORMULA
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G.f.: 4*(3-x)*(3-2*x)/(1-x)^3.
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EXAMPLE
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For n = 1, 4*(n^2+6*n+2) = 4*9 = 36 and 36^3+28*36^2 = 82944 = 288^2; for n = 38, 4*(n^2+6*n+2) = 4*1674 = 6696 and 6696^3+28*6696^2 = 301480061184 = 549072^2.
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PROGRAM
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(MAGMA) [ 4*(n+3)^2-28: n in [1..45] ];
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CROSSREFS
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Cf. A144562 (T(m,n)=2m*n+m+n-1), A028881 (n^2-7), A155135 (n^3+28*n^2 is a square), A155136 (n+28 is a square), A067076 (2n+3 is prime), A153238 (2n+3 is not prime).
Sequence in context: A043370 A044483 A031479 this_sequence A119843 A066216 A032497
Adjacent sequences: A153639 A153640 A153641 this_sequence A153643 A153644 A153645
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 30 2008
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EXTENSIONS
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Edited and extended by Klaus Brockhaus, Jan 21 2009
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