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A162622
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Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^4 - 1.
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11
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0, 1, 1, 2, 17, 32, 3, 83, 163, 243, 4, 259, 514, 769, 1024, 5, 629, 1253, 1877, 2501, 3125, 6, 1301, 2596, 3891, 5186, 6481, 7776, 7, 2407, 4807, 7207, 9607, 12007, 14407, 16807, 8, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768, 9, 6569, 13129
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OFFSET
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0,4
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COMMENTS
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Note that the last term of the n-th row is the 5th power of n, A000584(n).
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LINKS
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FORMULA
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Sum_{k=0..n} T(n,k) = n*(n+1)*(1+n^4)/2 (row sums). [R. J. Mathar, Jul 20 2009]
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EXAMPLE
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Triangle begins:
0;
1, 1;
2, 17, 32;
3, 83, 163, 243;
4, 259, 514, 769, 1024;
5, 629, 1253, 1877, 2501, 3125;
6, 1301, 2596, 3891, 5186, 6481, 7776;
7, 2407, 4807, 7207, 9607, 12007, 14407, 16807;
8, 4103, 8198, 12293, 16388, 20483, 24578, 28673, 32768;
9, 6569, 13129, 19689, 26249, 32809, 39369, 45929, 52489, 59049; etc.
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MAPLE
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MATHEMATICA
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Flatten[Table[NestList[#+n^4-1&, n, n], {n, 0, 9}]] (* Harvey P. Dale, Jun 23 2013 *)
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PROG
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(Magma) /* Triangle: */ [[n+k*(n^4-1): k in [0..n]]: n in [0..10]]; // Bruno Berselli, Dec 14 2012
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CROSSREFS
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Cf. A000583, A000584, A123865, A159797, A162609, A162610, A162611, A162612, A162613, A162614, A162615, A162616, A162623, A162624.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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