Original entry on oeis.org
1, 2, 4, 9, 24, 78, 317, 1636, 10752, 89871, 955536, 12930172, 222618065, 4874855542, 135781292308, 4811103270053, 216847500834512, 12432143862756778, 906625645142897789, 84102571511631809864, 9923979699312024569440, 1489546408205976627946331
Offset: 0
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[&+[Fibonacci(n-k+2)^k: k in [0..n]]: n in [0..21]]; // Bruno Berselli, Mar 28 2012
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Table[Sum[Fibonacci[n - k + 2]^k, {k, 0, n}], {n, 0, 100}]
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makelist(sum(fib(n-k+2)^k,k,0,n),n,0,12);
A067966
Number of binary arrangements without adjacent 1's on n X n array connected n-s.
Original entry on oeis.org
1, 2, 9, 125, 4096, 371293, 85766121, 52523350144, 83733937890625, 350356403707485209, 3833759992447475122176, 109879109551310452512114617, 8243206936713178643875538610721, 1619152874321527556575810000000000000
Offset: 0
Neighbors for n=4:
o o o o
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o o o o
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o o o o
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o o o o
Cf. circle
A000204, line
A000045, arrays: ne-sw nw-se
A067965, e-w ne-sw nw-se
A067963, n-s nw-se
A067964, e-w n-s nw-se
A066864, e-w ne-sw n-s nw-se
A063443, e-w n-s
A006506, nw-se
A067962, toruses: bare
A002416, ne-sw nw-se
A067960, ne-sw n-s nw-se
A067959, e-w ne-sw n-s nw-se
A067958, n-s
A067961, e-w n-s
A027683, e-w ne-sw n-s
A066866.
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[Fibonacci(n+2)^n: n in [0..13]]; // Bruno Berselli, Mar 28 2012
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Table[Fibonacci[n+2]^n, {n, 0, 100}]
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makelist(fib(n+2)^n, n, 0, 14);
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a(n)=fibonacci(n+2)^n \\ Charles R Greathouse IV, Mar 28 2012
A210343
a(n) = Fibonacci(n+1)^n.
Original entry on oeis.org
1, 1, 4, 27, 625, 32768, 4826809, 1801088541, 1785793904896, 4605366583984375, 31181719929966183601, 552061438912436417593344, 25601832525455335435322705761, 3107689015140868348741078056241817, 987683253336131809511244100000000000000
Offset: 0
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[Fibonacci(n+1)^n: n in [0..14]]; // Bruno Berselli, Mar 28 2012
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a:= n-> (<<1|1>, <1|0>>^n)[1,1]^n:
seq(a(n), n=0..15); # Alois P. Heinz, Dec 05 2015
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Table[Fibonacci[n+1]^n,{n,0,100}]
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makelist(fib(n+1)^n,n,0,14);
A210574
Lower triangular matrix in the LU-decomposition of the Vandermonde determinants generated by Fibonacci numbers.
Original entry on oeis.org
1, 1, 1, 1, 3, 1, 1, 7, 12, 1, 1, 15, 50, 264, 1, 1, 31, 180, 1920, 11970, 1, 1, 63, 602, 11760, 146160, 1689600, 1, 1, 127, 1932, 66024, 1477980, 34214400, 603233280, 1, 1, 255, 6050, 353304, 13556970, 568656000, 20043279360, 586244602944, 1
Offset: 0
The triangle begins:
1
1, 1
1, 3, 1
1, 7, 12, 1
1, 15, 50, 264, 1
1, 31, 180, 1920, 11970, 1
1, 63, 602, 11760, 146160, 1689600, 1
1, 127, 1932, 66024, 1477980, 34214400, 603233280, 1
1, 255, 6050, 353304, 13556970, 568656000, 20043279360, 586244602944, 1
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n = 10; f = Fibonacci[Range[2, n + 1]]; m = Outer[ Power, f, Range[0, n - 1]]; mi = Transpose[LUDecomposition[m][[1]]]; Flatten[Table[Append[Take[mi[[i]], i - 1], 1], {i, n}]] (* T. D. Noe, Mar 22 2012 *)
Showing 1-4 of 4 results.
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