A005204
Coding a recurrence.
Original entry on oeis.org
0, 0, 0, 1, 2, 4, 9, 38, 308, 4937, 316006, 161795380, 1325427757897, 694905868332618342, 186537373642942364470529332, 410200022670422956346283949740775609161, 472928427326946774459561651845917849178636866326243365478
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Cf.
A005203 (same kind of encoding).
-
A000930(n) = sum(i=0, n\3, binomial(n-2*i, i))
a(n) = if (n==0, 0, if (n==1, 0, if (n==2, 0, if (n==3, 1, 2^A000930(n-4)*a(n-1) + a(n-3))))) \\ Michel Marcus, Jul 29 2013
a(10) corrected and sequence extended by
Michel Marcus, Jul 29 2013
A144288
Fibonacci rabbit sequence number n coded in base n, also diagonal of A144287.
Original entry on oeis.org
1, 2, 10, 276, 81901, 2247615258, 81658169024988865, 644986443956439734064225751112, 3427833941153173630835645403655873661712817810325122
Offset: 1
-
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-> f(n, n)[1]: seq(a(n), n=1..11);
-
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]]}]; a[n_] := f[n, n][[1]]; Table[a[n], {n, 1, 9}] (* Jean-François Alcover, Jan 03 2013, translated from Maple *)
A162438
a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is maximized. a(n) = the decimal equivalent of the resulting binary number.
Original entry on oeis.org
1, 2, 6, 26, 218, 7002, 1792858, 14687099738, 30801080592587610, 529158535306496354546309978, 19064945459410035469668296404984822042942298
Offset: 1
The binary representation of the first few terms: 1, 10, 110, 11010, 11011010.
-
a[1] = 1; a[2] = 2; a[n_] := Block[ {a1 = IntegerDigits[a[n - 1], 2], a2 = IntegerDigits[ a[n - 2], 2]}, Max[ FromDigits[ Join[a1, a2], 2], FromDigits[ Join[a2, a1], 2]]]; Array[a, 13] (* Robert G. Wilson v, Jul 27 2009 *)
A065353
Decimal representation of palindromes extracted from the Golden String using ever increasing Fibonacci-style subdivisions.
Original entry on oeis.org
1, 0, 3, 2, 27, 90, 7003, 744282, 14687099739, 12786682083105626, 529158535306496354546309979, 7914572860144723898900437268660641289952090
Offset: 0
Bin (Dec) -> 1 (1); 0 (0); 11 (3); 010 (2); 11011 (27); 01011010 (90); 1101101011011 (7003); 010110101101101011010 (744282); etc.
A065354
Decimal representation of binary palindromes extracted from the Golden String using ever-increasing Lucas-style subdivisions.
Original entry on oeis.org
1, 5, 6, 107, 730, 224091, 190536538, 120316721060699, 26815615903949132618586, 9090874414162652716478489106641017691, 285152539069955354427985396951391834474389843433339258362714
Offset: 1
Bin (Dec) -> {10} skipped -> start: 1 (1); 101 (5); 0110 (6); 1101011 (107); 01011011010 (730); 110110101101011011 (224091); etc.
A162437
a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is minimized. a(n) = the decimal equivalent of the resulting binary number.
Original entry on oeis.org
1, 2, 5, 21, 173, 5549, 1420717, 11638517165, 24407739551034797, 419321772563920711635545517, 15107659029337673520218077770654501397966253
Offset: 1
The binary representation of the first few terms: 1, 10, 101, 10101, 10101101
-
a[1] = 1; a[2] = 2; a[n_] := Block[{a1 = IntegerDigits[ a[n - 1], 2], a2 = IntegerDigits[ a[n - 2], 2]}, Min[ FromDigits[ Join[a1, a2], 2], FromDigits[ Join[a2, a1], 2]]]; Array[a, 13] (* Robert G. Wilson v, Jul 27 2009 *)
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