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 A277666 Number A(n,k) of n-length words over a k-ary alphabet {a_1,a_2,...,a_k} avoiding consecutive letters a_i, a_{i+1}; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 7, 4, 1, 0, 1, 5, 13, 16, 5, 1, 0, 1, 6, 21, 42, 37, 6, 1, 0, 1, 7, 31, 88, 136, 86, 7, 1, 0, 1, 8, 43, 160, 369, 440, 200, 8, 1, 0, 1, 9, 57, 264, 826, 1547, 1423, 465, 9, 1, 0, 1, 10, 73, 406, 1621, 4264, 6486, 4602, 1081, 10, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened FORMULA G.f. of column k: 1/(1 + Sum_{j=1..k} (k+1-j)*(-x)^j). EXAMPLE A(3,3) = 16: 000, 002, 020, 021, 022, 100, 102, 110, 111, 200, 202, 210, 211, 220, 221, 222 (using ternary alphabet {0, 1, 2}). Square array A(n,k) begins:   1, 1, 1,   1,    1,     1,      1,      1, ...   0, 1, 2,   3,    4,     5,      6,      7, ...   0, 1, 3,   7,   13,    21,     31,     43, ...   0, 1, 4,  16,   42,    88,    160,    264, ...   0, 1, 5,  37,  136,   369,    826,   1621, ...   0, 1, 6,  86,  440,  1547,   4264,   9953, ...   0, 1, 7, 200, 1423,  6486,  22012,  61112, ...   0, 1, 8, 465, 4602, 27194, 113632, 375231, ... MAPLE A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,       -add((-1)^j*(k+1-j)*A(n-j, k), j=1..k)))     end: seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1, -Sum[(-1)^j*(k + 1 - j)* A[n-j, k], {j, 1, k}]]]; Table[A[n, d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jun 08 2018, from Maple *) CROSSREFS Columns k=0-10 give: A000007, A000012, A000027(n+1), A095263(n+1), A277667, A277668, A277669, A277670, A277671, A277672, A096261. Rows n=0-2 give: A000012, A001477, A002061 (for k>0). Main diagonal gives A277673. Sequence in context: A339779 A277504 A167763 * A274581 A321919 A321918 Adjacent sequences:  A277663 A277664 A277665 * A277667 A277668 A277669 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Oct 26 2016 STATUS approved

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Last modified January 22 23:50 EST 2022. Contains 350504 sequences. (Running on oeis4.)