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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.
12
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
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
Rows n=1-3 give: A000012, A001477, A002522.
Main diagonal gives A144288.
Sequence in context: A106179 A081572 A292630 * A106196 A037027 A182810
KEYWORD
base,nice,nonn,tabl
AUTHOR
Alois P. Heinz, Sep 17 2008
STATUS
approved