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

1,5

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.

Links

Table of n, a(n) for n=1..66.

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

Example

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

Mathematica

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

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.

Sequence in context: A205497 A063394 A344527 * A108470 A328300 A157152

Adjacent sequences: A193868 A193869 A193870 * A193872 A193873 A193874

Keyword

nonn,tabl,easy

Author

Omar E. Pol, Aug 21 2011

Status

approved