login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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