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 A179647 Rectangular array read by antidiagonals: T(n,k) is the number of compositions (ordered partitions) of n in which no part (summand) is equal to k. 1
 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 3, 4, 3, 1, 2, 4, 6, 7, 5, 1, 2, 4, 7, 11, 12, 8, 1, 2, 4, 8, 14, 21, 21, 13, 1, 2, 4, 8, 15, 27, 39, 37, 21, 1, 2, 4, 8, 16, 30, 52, 73, 65, 34, 1, 2, 4, 8, 16, 31, 59, 101, 136, 114, 55, 1, 2, 4, 8, 16, 32, 62, 116, 195, 254, 200, 89 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Alois P. Heinz, Antidiagonals n = 1..141, flattened FORMULA O.g.f. for column k: B(A(x)) where A(x) = x/(1-x)-x^k and B(x) = 1/(1-x). EXAMPLE T(4,2) = 4 because there are four compositions of 4 with no part equal to two: 4, 3+1, 1+3, 1+1+1+1. Array starts as: 0,    1,   1,   1,   1,   1,   1,   1,   1,   1, ... 1,    1,   2,   2,   2,   2,   2,   2,   2,   2, ... 1,    2,   3,   4,   4,   4,   4,   4,   4,   4, ... 2,    4,   6,   7,   8,   8,   8,   8,   8,   8, ... 3,    7,  11,  14,  15,  16,  16,  16,  16,  16, ... 5,   12,  21,  27,  30,  31,  32,  32,  32,  32, ... 8,   21,  39,  52,  59,  62,  63,  64,  64,  64, ... 13,  37,  73, 101, 116, 123, 126, 127, 128, 128, ... 21,  65, 136, 195, 228, 244, 251, 254, 255, 256, ... 34, 114, 254, 377, 449, 484, 500, 507, 510, 511, ... MAPLE T:= proc(n, k) option remember;       `if`(n=0, 1, add(`if`(j=k, 0, T(n-j, k)), j=1..n))     end: seq(seq(T(n, d+1-n), n=1..d), d=1..12);  # Alois P. Heinz, Oct 23 2011 MATHEMATICA Transpose[Table[Table[Length[Select[Level[Map[Permutations, IntegerPartitions[n]], {2}], FreeQ[#, i] &]], {n, 1, 10}], {i, 1, 10}]] // Grid (* second program: *) a = x/(1 - x) - x^n; Transpose[Table[Rest[CoefficientList[Series[1/(1 - a), {x, 0, 10}], x]], {n, 1, 10}]] // Grid CROSSREFS Sequence in context: A261904 A297030 A266348 * A029330 A132225 A263923 Adjacent sequences:  A179644 A179645 A179646 * A179648 A179649 A179650 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Jan 09 2011 EXTENSIONS Corrected and extended by Alois P. Heinz, Oct 23 2011 STATUS approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)