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A162616
Triangle read by rows in which row n lists n terms, starting with n^3 + n - 1, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).
6
1, 9, 16, 29, 55, 81, 67, 130, 193, 256, 129, 253, 377, 501, 625, 221, 436, 651, 866, 1081, 1296, 349, 691, 1033, 1375, 1717, 2059, 2401, 519, 1030, 1541, 2052, 2563, 3074, 3585, 4096, 737, 1465, 2193, 2921, 3649, 4377, 5105, 5833, 6561, 1009, 2008
OFFSET
1,2
COMMENTS
Note that the last term of the n-th row is the fourth power of n, A000583(n).
See also the triangles of A162614 and A162615.
LINKS
FORMULA
Row sums: n*(n^2 + n - 1)*(n^2+1)/2. - R. J. Mathar, Jul 20 2009
EXAMPLE
Triangle begins:
1;
9, 16;
29, 55, 81;
67, 130, 193, 256;
129, 253, 377, 501, 625;
221, 436, 651, 866, 1081, 1296;
...
MAPLE
A162616 := proc(n, k) n^3+n-1+(k-1)*(n^3-1) ; end proc: seq(seq(A162616(n, k), k=1..n), n=1..15) ; # R. J. Mathar, Feb 05 2010
MATHEMATICA
Table[NestList[#+n^3-1&, n^3+n-1, n-1], {n, 10}]//Flatten (* Harvey P. Dale, Dec 17 2021 *)
KEYWORD
easy,nonn,tabl
AUTHOR
Omar E. Pol, Jul 12 2009
EXTENSIONS
More terms from R. J. Mathar, Feb 05 2010
STATUS
approved