cp's OEIS Frontend

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.

%I A144287 #34 Jan 05 2025 19:51:38
%S A144287 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,
%T A144287 13,1,7,37,655,17681,612696,1488565,21,1,8,50,1338,81901,18105620,
%U A144287 4019900977,12194330294,34,1,9,65,2457,289045,255941280,1186569930001,6409020585966267,25573364166211253,55
%N 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.
%H A144287 Alois P. Heinz, <a href="/A144287/b144287.txt">Antidiagonals n = 1..16, flattened</a>
%H A144287 H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-4/gould.pdf">Sequences associated with t-ary coding of Fibonacci's rabbits</a>, Fib. Quart., 15 (1977), 311-318.
%F A144287 See program.
%e A144287 Square array begins:
%e A144287   1,   1,    1,     1,     1,  ...
%e A144287   1,   2,    3,     4,     5,  ...
%e A144287   2,   5,   10,    17,    26,  ...
%e A144287   3,  22,   93,   276,   655,  ...
%e A144287   5, 181, 2521, 17681, 81901,  ...
%p A144287 f:= proc(n,b) option remember; `if`(n<2, [n,n], [f(n-1, b)[1]*
%p A144287        b^f(n-1, b)[2] +f(n-2, b)[1], f(n-1, b)[2] +f(n-2, b)[2]])
%p A144287     end:
%p A144287 A:= (n,k)-> f(n,k)[1]:
%p A144287 seq(seq(A(n, 1+d-n), n=1..d), d=1..11);
%t A144287 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 *)
%Y A144287 Columns k=1-10 give: A000045, A005203, A005205, A320986, A320987, A320988, A320989, A320990, A320991, A061107 and A036299.
%Y A144287 Rows n=1-3 give: A000012, A001477, A002522.
%Y A144287 Main diagonal gives A144288.
%K A144287 base,nice,nonn,tabl
%O A144287 1,5
%A A144287 _Alois P. Heinz_, Sep 17 2008