cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Views

Author

R. H. Hardin, Feb 02 2002

Keywords

Comments

Central coefficients of triangle A210341.

Examples

			Neighbors for n=4:
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o
| | | |
| | | |
o o o o

Links

Crossrefs

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.
Cf. A100399, A210343, A210341.

Programs

  • Magma
    [Fibonacci(n+2)^n: n in [0..13]]; // Bruno Berselli, Mar 28 2012
  • Mathematica
    Table[Fibonacci[n+2]^n, {n, 0, 100}]
  • Maxima
    makelist(fib(n+2)^n, n, 0, 14);
  • PARI
    a(n)=fibonacci(n+2)^n \\ Charles R Greathouse IV, Mar 28 2012

Formula

a(n) = F(n+2)^n, where F(n) = A000045(n) is the n-th Fibonacci number.
a(n) ~ phi^2/sqrt(5) phi^n^2. [Charles R Greathouse IV, Mar 28 2012]

Extensions

Edited by Dean Hickerson, Feb 15 2002

A103323 Square array T(n,k) read by antidiagonals: powers of Fibonacci numbers.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 9, 5, 1, 1, 16, 27, 25, 8, 1, 1, 32, 81, 125, 64, 13, 1, 1, 64, 243, 625, 512, 169, 21, 1, 1, 128, 729, 3125, 4096, 2197, 441, 34, 1, 1, 256, 2187, 15625, 32768, 28561, 9261, 1156, 55, 1, 1, 512, 6561, 78125, 262144, 371293, 194481, 39304, 3025, 89
Offset: 1

Views

Author

Ralf Stephan, Feb 02 2005

Keywords

Comments

Number of ways to create subsets S(1), S(2),..., S(k-1) such that S(1) is in [n] and for 2<=i<=k-1, S(i) is in [n] and S(i) is disjoint from S(i-1).

Examples

			Square array T(n,k) begins:
  1, 1,  2,   3,     5,      8, ...
  1, 1,  4,   9,    25,     64, ...
  1, 1,  8,  27,   125,    512, ...
  1, 1, 16,  81,   625,   4096, ...
  1, 1, 32, 243,  3125,  32768, ...
  1, 1, 64, 729, 15625, 262144, ...
  ...

References

  • A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, identity 138.

Links

Crossrefs

Rows include A000045, A007598, A056570, A056571, A056572, A056573, A056574.
Main diagonal gives A100399.
Cf. A244003.
Cf. A105317, A254719.

Programs

  • Maple
    A:= (n, k)-> (<<1|1>, <1|0>>^n)[1, 2]^k:
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);  # Alois P. Heinz, Jun 17 2014
  • Mathematica
    T[n_, k_] := Fibonacci[k]^n; Table[T[n-k+1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 16 2015 *)
  • PARI
    T(n,k)=fibonacci(k)^n

Formula

T(n, k) = A000045(k)^n, n, k > 0.
T(n, k) = Sum[i_1>=0, Sum[i_2>=0, ... Sum[i_{k-1}>=0, C(n, i_1)*C(n-i_1, i_2)*C(n-i_2, i_3)*...*C(n-i_{k-2}, i_{k-1}) ] ... ]].

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

Views

Author

Emanuele Munarini, Mar 20 2012

Keywords

Links

Crossrefs

Cf. A100399, A067966, A210341, A210342.

Programs

  • Magma
    [Fibonacci(n+1)^n: n in [0..14]]; // Bruno Berselli, Mar 28 2012
  • Maple
    a:= n-> (<<1|1>, <1|0>>^n)[1,1]^n:
seq(a(n), n=0..15);  # Alois P. Heinz, Dec 05 2015
  • Mathematica
    Table[Fibonacci[n+1]^n,{n,0,100}]
  • Maxima
    makelist(fib(n+1)^n,n,0,14);

A152915 Exponacci (or exponential Fibonacci) numbers.

Original entry on oeis.org

1, 1, 2, 9, 64, 3125, 1679616, 96889010407, 9223372036854775808, 278128389443693511257285776231761, 10000000000000000000000000000000000000000000000000000000
Offset: 0

Views

Author

ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 15 2008

Keywords

Examples

			a(9) = 9 ^ Fibonacci(9) = 9 ^ 34 = 278128389443693511257285776231761.

Links

Crossrefs

Cf. A000045, A100399.
Main diagonal of A244003.

Programs

  • Magma
    [n^Fibonacci(n): n in [1..10]]; // Vincenzo Librandi, Apr 05 2017
  • Maple
    a:= n-> n^(<<1|1>, <1|0>>^n)[1, 2]:
seq(a(n), n=0..12);  # Alois P. Heinz, Jun 17 2014
  • Mathematica
    Array[ #^Fibonacci[ # ]&,12] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2010 *)
  • Other
    unsigned long Exponacci(unsigned int n)
{
if (n == 0)
return 1;
return pow(n, Fibonacci(n));
}

Formula

a(0) = 1, a(n) = n ^ Fibonacci(n) for n > 0; Fibonacci = A000045.

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Apr 03 2010

A182148 a(n) = Fibonacci(n-1)^n.

Original entry on oeis.org

1, 0, 1, 1, 16, 243, 15625, 2097152, 815730721, 794280046581, 2064377754059776, 13931233916552734375, 246990403565262140303521, 11447545997288281555215581184, 1389897885974444705448234373058929, 441692732032956477538220683055593208393
Offset: 0

Views

Author

Vincenzo Librandi, Jul 04 2012

Keywords

Links

Crossrefs

Cf. A000045, A100399, A210343.

Programs

  • Magma
    [Fibonacci(n-1)^n: n in [0..15]];
  • Mathematica
    Table[Fibonacci[n-1]^n,{n,0,20}]

A325174 a(n) = Fibonacci(n)^n mod prime(n).

Original entry on oeis.org

1, 1, 3, 4, 1, 12, 4, 9, 19, 5, 27, 10, 30, 36, 46, 16, 27, 34, 58, 32, 9, 62, 2, 1, 53, 92, 30, 35, 76, 52, 9, 4, 70, 81, 105, 59, 61, 90, 82, 139, 19, 29, 28, 81, 92, 1, 121, 34, 155, 165, 1, 36, 178, 103, 230, 50, 266, 106, 135, 222, 272, 4, 72, 253, 182, 308, 20, 32, 166, 206
Offset: 1

Views

Author

Vincenzo Librandi, Apr 15 2019

Keywords

Links

Crossrefs

Cf. A000040, A000045, A072123, A100399.

Programs

  • Magma
    [Modexp(Fibonacci(n), n, NthPrime(n)): n in [1..70]];
  • Maple
    a:= n-> ((<<0|1>, <1|1>>^n)[2, 1]) &^n mod ithprime(n):
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 15 2019
  • Mathematica
    Table[PowerMod[Fibonacci[n], n, Prime[n]], {n, 70}]
  • PARI
    a(n) = lift(Mod(fibonacci(n), prime(n))^n); \\ Michel Marcus, Apr 16 2019
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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