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 A255212 Number A(n,k) of partitions of n^2 into at most k square parts; square array A(n,k), n>=0, k>=0, read by antidiagonals. 12
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 2, 3, 3, 3, 2, 1, 1, 0, 1, 1, 2, 3, 3, 4, 4, 2, 1, 1, 0, 1, 1, 2, 3, 4, 5, 5, 4, 1, 1, 1, 0, 1, 1, 2, 4, 5, 7, 9, 6, 2, 4, 2, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,24 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened EXAMPLE Square array A(n,k) begins:   1, 1, 1, 1, 1,  1,  1,  1,  1,  1,  1, ...   0, 1, 1, 1, 1,  1,  1,  1,  1,  1,  1, ...   0, 1, 1, 1, 2,  2,  2,  2,  2,  2,  2, ...   0, 1, 1, 2, 2,  2,  3,  3,  3,  4,  4, ...   0, 1, 1, 1, 2,  3,  3,  4,  5,  5,  6, ...   0, 1, 2, 2, 3,  4,  5,  7,  8,  9, 11, ...   0, 1, 1, 2, 4,  5,  9, 10, 11, 15, 17, ...   0, 1, 1, 2, 4,  6,  9, 13, 18, 21, 27, ...   0, 1, 1, 1, 2,  7,  9, 16, 25, 30, 41, ...   0, 1, 1, 4, 6,  8, 18, 27, 36, 52, 68, ...   0, 1, 2, 2, 7, 13, 23, 36, 51, 70, 94, ... MAPLE b:= proc(n, i, t) option remember; `if`(n=0 or i=1 and n<=t, 1,       (j-> `if`(t*jn, 0, b(n-j, i, t-1))))(i^2))     end: A:= (n, k)-> b(n^2, n, k): seq(seq(A(n, d-n), n=0..d), d=0..15); MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n == 0 || i == 1 && n <= t, 1, Function[j, If[t*jn, 0, b[n-j, i, t-1]]]][i^2]]; A[n_, k_] := b[n^2, n, k]; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 15}] // Flatten (* Jean-François Alcover, Feb 22 2016, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000007, A000012, A063014, A016727, A065458, A065459, A065460, A065461, A065462, A255213, A255214. Main diagonal gives A105152. Sequence in context: A099918 A099860 A317950 * A323011 A327747 A282750 Adjacent sequences:  A255209 A255210 A255211 * A255213 A255214 A255215 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Feb 17 2015 STATUS approved

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Last modified August 9 12:53 EDT 2020. Contains 336323 sequences. (Running on oeis4.)