A144287 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) = Fibonacci rabbit sequence number n coded in base k.

1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 10, 22, 5, 1, 5, 17, 93, 181, 8, 1, 6, 26, 276, 2521, 5814, 13, 1, 7, 37, 655, 17681, 612696, 1488565, 21, 1, 8, 50, 1338, 81901, 18105620, 4019900977, 12194330294, 34, 1, 9, 65, 2457, 289045, 255941280, 1186569930001, 6409020585966267, 25573364166211253, 55

Offset

1,5

Links

Alois P. Heinz, Antidiagonals n = 1..16, flattened

H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., Sequences associated with t-ary coding of Fibonacci's rabbits, Fib. Quart., 15 (1977), 311-318.

Formula

See program.

Example

Square array begins:
  1,   1,    1,     1,     1,  ...
  1,   2,    3,     4,     5,  ...
  2,   5,   10,    17,    26,  ...
  3,  22,   93,   276,   655,  ...
  5, 181, 2521, 17681, 81901,  ...

Maple

f:= proc(n, b) option remember; `if`(n<2, [n, n], [f(n-1, b)[1]*
       b^f(n-1, b)[2] +f(n-2, b)[1], f(n-1, b)[2] +f(n-2, b)[2]])
    end:
A:= (n, k)-> f(n, k)[1]:
seq(seq(A(n, 1+d-n), n=1..d), d=1..11);

Mathematica

f[n_, b_] := f[n, b] = If[n < 2, {n, n}, {f[n-1, b][[1]]*b^f[n-1, b][[2]] + f[n-2, b][[1]], f[n-1, b][[2]] + f[n-2, b][[2]]}]; t[n_, k_] := f[n, k][[1]]; Flatten[ Table[t[n, 1+d-n], {d, 1, 11}, {n, 1, d}]] (* Jean-François Alcover, translated from Maple, Dec 09 2011 *)

Crossrefs

Columns k=1-10 give: A000045, A005203, A005205, A320986, A320987, A320988, A320989, A320990, A320991, A061107 and A036299.

Rows n=1-3 give: A000012, A001477, A002522.

Main diagonal gives A144288.

Sequence in context: A106179 A081572 A292630 * A106196 A037027 A182810

Adjacent sequences: A144284 A144285 A144286 * A144288 A144289 A144290

Keyword

base,nice,nonn,tabl

Author

Alois P. Heinz, Sep 17 2008

Status

approved