cp's OEIS Frontend

A212835 T(n,k)=Number of 0..k arrays of length n+1 with 0 never adjacent to k.

%I A212835 #6 Jul 22 2025 22:58:38
%S A212835 2,7,2,14,17,2,23,50,41,2,34,107,178,99,2,47,194,497,634,239,2,62,317,
%T A212835 1106,2309,2258,577,2,79,482,2137,6306,10727,8042,1393,2,98,695,3746,
%U A212835 14407,35954,49835,28642,3363,2,119,962,6113,29114,97127,204994,231521
%N A212835 T(n,k)=Number of 0..k arrays of length n+1 with 0 never adjacent to k.
%C A212835 Table starts
%C A212835 .2.....7......14.......23........34.........47.........62..........79
%C A212835 .2....17......50......107.......194........317........482.........695
%C A212835 .2....41.....178......497......1106.......2137.......3746........6113
%C A212835 .2....99.....634.....2309......6306......14407......29114.......53769
%C A212835 .2...239....2258....10727.....35954......97127.....226274......472943
%C A212835 .2...577....8042....49835....204994.....654797....1758602.....4159927
%C A212835 .2..1393...28642...231521...1168786....4414417...13667858....36590017
%C A212835 .2..3363..102010..1075589...6663906...29760487..106226618...321839625
%C A212835 .2..8119..363314..4996919..37994674..200635007..825593474..2830847119
%C A212835 .2.19601.1293962.23214443.216628994.1352612477.6416514026.24899654327
%H A212835 R. H. Hardin, <a href="/A212835/b212835.txt">Table of n, a(n) for n = 1..9999</a>
%F A212835 Empirical for column k: a(n) = k*a(n-1) +(k-1)*a(n-2)
%F A212835 Empirical for rows:
%F A212835 n=1: a(k) = k^2 + 2*k - 1
%F A212835 n=2: a(k) = k^3 + 3*k^2 - k - 1
%F A212835 n=3: a(k) = k^4 + 4*k^3 - 4*k + 1
%F A212835 n=4: a(k) = k^5 + 5*k^4 + 2*k^3 - 8*k^2 + k + 1
%F A212835 n=5: a(k) = k^6 + 6*k^5 + 5*k^4 - 12*k^3 - 3*k^2 + 6*k - 1
%F A212835 n=6: a(k) = k^7 + 7*k^6 + 9*k^5 - 15*k^4 - 13*k^3 + 15*k^2 - k - 1
%F A212835 n=7: a(k) = k^8 + 8*k^7 + 14*k^6 - 16*k^5 - 30*k^4 + 24*k^3 + 8*k^2 - 8*k + 1
%e A212835 Some solutions for n=5 k=4
%e A212835 ..1....4....1....1....1....3....2....1....1....4....3....1....0....2....2....3
%e A212835 ..1....3....0....4....2....4....1....1....2....2....3....4....1....3....3....1
%e A212835 ..1....3....3....1....3....3....2....2....2....4....3....3....1....1....0....3
%e A212835 ..1....3....0....4....2....3....3....3....4....2....2....0....4....4....2....1
%e A212835 ..1....4....0....3....2....2....3....3....4....4....0....1....4....3....4....2
%e A212835 ..1....2....0....4....3....1....0....2....4....2....3....2....1....4....3....4
%Y A212835 Column 2 is A001333(n+2)
%Y A212835 Column 3 is A055099(n+1)
%Y A212835 Column 4 is A126473(n+1)
%Y A212835 Column 5 is A126501(n+1)
%Y A212835 Column 6 is A126528(n+1)
%Y A212835 Row 1 is A008865(n+1)
%K A212835 nonn,tabl
%O A212835 1,1
%A A212835 _R. H. Hardin_ May 28 2012