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 1-4 of 4 results.

A249184 A249183 seen as binary numbers.

Original entry on oeis.org

1, 7, 27, 119, 427, 1799, 6939, 30583, 109227, 458759, 1769499, 7798903, 27984299, 117901063, 454761243, 2004318071, 7158278827, 30064771079, 115964117019, 511101108343, 1833951035819, 7726646167303, 29802778073883, 131352984844151, 469126392949419
Offset: 0

Views

Author

Reinhard Zumkeller, Nov 14 2014

Keywords

Comments

Appears to be basically the same as A048711. - R. J. Mathar, Nov 16 2014

Links

Crossrefs

Cf. A249183 (binary), A249133, A007088, A001317, A000120, A023416, A105321, A249304.

Programs

  • Haskell
    a249184 = foldr (\b v -> 2 * v + b) 0 . a249133_row
  • Mathematica
    a[n_] := FromDigits[Mod[Riffle[Binomial[n, Range[0, n]], Binomial[n - 1, Range[0, n - 1]]], 2], 2]; Array[a, 25, 0] (* Amiram Eldar, Jul 28 2023 *)

Formula

a(n) = Sum_{k=0..2*n} (A249133(n,k)*2^k).
A007088(a(n)) = A249183(n).
A000120(a(n)) = A105321(n).
A023416(a(n)) = A249304(n).

A048710 Family 1 "Rule 90 x Rule 150 Array" read by antidiagonals.

Original entry on oeis.org

1, 5, 7, 17, 27, 21, 85, 119, 65, 107, 257, 427, 325, 455, 273, 1285, 1799, 1105, 1755, 1365, 1911, 4369, 6939, 5397, 7607, 4097, 6827, 5189, 21845, 30583, 16705, 27499, 20485, 28679, 17745, 28123, 65537
Offset: 0

Views

Author

Antti Karttunen, Mar 18 1999

Keywords

Comments

Infinitely many one-dimensional cellular automaton rules (given in sequence A048705) occur in this array, as combinations of CA-rules "90" (generates rows) and "150" (generates columns).
No pattern occurs twice in such arrays.
Each row/column can be generated from its predecessor row/column with SHIFTXORADJ transformation, given in A048711.

Examples

			   1  5  17   85  257 1105 ... [ beginning of array ]
   7 27 119  427 1799 ...
  21 65 325 1105 5397 ...

Links

Crossrefs

Rows = A038183, A048711, A048713, columns = A038184, A048712, A048713, diagonal = A048709. Cf. A048720.

Programs

  • Maple
    trinv := n -> floor((1+sqrt(1+8*n))/2); # Gives integral inverses of the triangular numbers

Formula

a(n) = rule150(rule90(1, (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n)), (n-((trinv(n)*(trinv(n)-1))/2))).

A048712 2nd column of Family 1 "90 X 150 array": generations 0 .. n of Rule 150 starting from seed pattern 5.

Original entry on oeis.org

5, 27, 65, 455, 1365, 6827, 17745, 121527, 328965, 1776411, 4276545, 29804231, 89149525, 447852971, 1158943825, 7976283575, 21475164165, 115965886491, 279177134145, 1954239939015, 5862719817045
Offset: 0

Views

Author

Antti Karttunen

Keywords

Crossrefs

Cf. A048714. See A048711 for the definition of SHIFTXORADJ

Formula

SHIFTXORADJ(A038184)

A048713 3rd row of Family 1 "90 x 150 array": generations 0 .. n of Rule 90 starting from seed pattern 21.

Original entry on oeis.org

21, 65, 325, 1105, 5397, 16705, 83013, 283985, 1376277, 4259905, 21299525, 72418385, 353703189, 1094795585, 5440291909, 18611524945, 90194313237, 279172874305, 1395864371525, 4745938863185, 23179938501909
Offset: 0

Views

Author

Antti Karttunen

Keywords

Formula

SHIFTXORADJ(A048711)
Showing 1-4 of 4 results.

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

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