cp's OEIS Frontend

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

%I A193871 #31 May 12 2025 10:13:04
%S A193871 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,
%T A193871 1,1,127,727,1021,621,211,43,1,1,255,2185,4093,3121,1291,337,57,1,1,
%U A193871 511,6559,16381,15621,7771,2395,505,73,1,1,1023,19681,65533,78121,46651,16801,4089,721,91,1
%N A193871 Square array T(n,k) = k^n - k + 1 read by antidiagonals.
%C A193871 The columns give 1^n-0, 2^n-1, 3^n-2, 4^n-3, 5^n-4, etc.
%C A193871 The main diagonal gives A006091, which is a sequence related to the famous "coconuts" problem.
%H A193871 M. B. Richardson, <a href="https://dx.doi.org/10.15200/winn.147175.52128">A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Coconuts Problem</a>, The Winnower, 3 (2016), e147175.52128. doi: 10.15200/winn.147175.52128
%e A193871 Array begins:
%e A193871   1,   1,    1,     1,     1,    1,    1,   1,   1,   1
%e A193871   1,   3,    7,    13,    21,   31,   43,  57,  73
%e A193871   1,   7,   25,    61,   121,  211,  337, 505
%e A193871   1,  15,   79,   253,   621, 1291, 2395
%e A193871   1,  31,  241,  1021,  3121, 7771
%e A193871   1,  63,  727,  4093, 15621
%e A193871   1, 127, 2185, 16381
%e A193871   1, 255, 6559
%e A193871   1, 511
%e A193871   1
%t A193871 Table[k^# - k + 1 &[n - k + 1], {n, 11}, {k, n}] // Flatten (* _Michael De Vlieger_, Nov 16 2016 *)
%Y A193871 Row 1: A000012. Rows 2,3: A002061, A061600 but both without repetitions.
%Y A193871 Columns 1..10: A000012, positives A000225, A058481, A141725, A164785, A164784, A164783, A164786, A177095, A170955.
%Y A193871 Cf. A276135.
%K A193871 nonn,tabl,easy
%O A193871 1,5
%A A193871 _Omar E. Pol_, Aug 21 2011