A193871 Square array T(n,k) = k^n - k + 1 read by antidiagonals.

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 25, 13, 1, 1, 31, 79, 61, 21, 1, 1, 63, 241, 253, 121, 31, 1, 1, 127, 727, 1021, 621, 211, 43, 1, 1, 255, 2185, 4093, 3121, 1291, 337, 57, 1, 1, 511, 6559, 16381, 15621, 7771, 2395, 505, 73, 1, 1, 1023, 19681, 65533, 78121, 46651, 16801, 4089, 721, 91, 1

Offset: 1

Author

Omar E. Pol, Aug 21 2011

Keywords

• nonn
• tabl
• easy

Comments

The columns give 1^n-0, 2^n-1, 3^n-2, 4^n-3, 5^n-4, etc.

The main diagonal gives A006091, which is a sequence related to the famous "coconuts" problem.

Examples

			Array begins:
  1,   1,    1,     1,     1,    1,    1,   1,   1,   1
  1,   3,    7,    13,    21,   31,   43,  57,  73
  1,   7,   25,    61,   121,  211,  337, 505
  1,  15,   79,   253,   621, 1291, 2395
  1,  31,  241,  1021,  3121, 7771
  1,  63,  727,  4093, 15621
  1, 127, 2185, 16381
  1, 255, 6559
  1, 511
  1
		

Links

• M. B. Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Coconuts Problem, The Winnower, 3 (2016), e147175.52128. doi: 10.15200/winn.147175.52128

Crossrefs

Row 1: A000012. Rows 2,3: A002061, A061600 but both without repetitions.

Columns 1..10: A000012, positives A000225, A058481, A141725, A164785, A164784, A164783, A164786, A177095, A170955.

Cf. A276135.

Programs

Mathematica

Table[k^# - k + 1 &[n - k + 1], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Nov 16 2016 *)