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A144287
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Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) = Fibonacci rabbit sequence number n coded in base k.
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..136
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FORMULA
| See program.
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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, ...
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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: T:= (n, k)-> f(n, k)[1]: seq (seq (T(n, 1+d-n), n=1..d), d=1..11);
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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}]] (* From Jean-François Alcover, translated from Maple, Dec 09 2011 *)
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CROSSREFS
| Rows 1-3 give: A000012, A001477, A002522. Columns 1-3, 10 give: A000045, A005203, A005205, A061107 and A036299. Diagonal gives: A144288.
Sequence in context: A073133 A106179 A081572 * A106196 A037027 A182810
Adjacent sequences: A144284 A144285 A144286 * A144288 A144289 A144290
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KEYWORD
| base,nice,nonn,tabl
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AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 17 2008
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