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.

Previous Showing 11-17 of 17 results.

A211969 Triangle of decimal equivalents of binary numbers with some initial repeats, A211968.

Original entry on oeis.org

3, 6, 7, 10, 12, 13, 14, 15, 20, 21, 24, 25, 26, 27, 28, 29, 30, 31, 36, 40, 41, 42, 43, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106
Offset: 2

Views

Author

Omar E. Pol, Dec 03 2012

Keywords

Examples

			Irregular triangle begins, starting at row 2:
3;
6, 7;
10, 12, 13, 14, 15;
20, 21, 24, 25, 26, 27, 28, 29, 30, 31;
36, 40, 41, 42, 43, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63;

Links

Crossrefs

Complement of A211967.
Row lengths give: A093370.
Column 1 gives: A005418(n+1).
Right border gives: A000225(n).
Cf. A093370, A093371, A121880, A122536, A211027, A211029, A211973, A216955.

Programs

  • Maple
    s:= proc(n) s(n):= `if`(n=1, [[1]], map(x->
      [[x[], 0], [x[], 1]][], s(n-1))) end:
T:= proc(n) map (x-> add(x[i]*2^(nops(x)-i), i=1..nops(x)), select
      (proc(l) local i; for i to iquo(nops(l), 2) do if l[1..i]=
      l[i+1..2*i] then return true fi od; false end, s(n)))[] end:
seq (T(n), n=2..7);  # Alois P. Heinz, Dec 04 2012

A211967 Triangle of decimal equivalents of binary numbers with no initial repeats, A211027.

Original entry on oeis.org

1, 2, 4, 5, 8, 9, 11, 16, 17, 18, 19, 22, 23, 32, 33, 34, 35, 37, 38, 39, 44, 46, 47, 64, 65, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 88, 89, 92, 93, 94, 95, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 148, 149, 150
Offset: 1

Views

Author

Omar E. Pol, Nov 30 2012

Keywords

Examples

			Irregular triangle begins:
1;
2;
4,   5;
8,   9, 11;
16, 17, 18, 19, 22, 23;
32, 33, 34, 35, 37, 38, 39, 44, 46, 47;

Links

Crossrefs

Columns 1-2 give: A000079(n-1), A000051(n-1) for n>2. Row n has length A093371(n). Right border gives A083329(n-1).
Cf. A122536, A211029, A211968, A211969, A216955.

Programs

  • Maple
    s:= proc(n) s(n):= `if`(n=1, [[1]], map(x->
      [[x[], 0], [x[], 1]][], s(n-1))) end:
T:= proc(n) map (x-> add(x[i]*2^(nops(x)-i), i=1..nops(x)), select
      (proc(l) local i; for i to iquo(nops(l), 2) do if l[1..i]=
      l[i+1..2*i] then return false fi od; true end, s(n)))[] end:
seq (T(n), n=1..8);  # Alois P. Heinz, Dec 03 2012

A211973 a(n) = A121880(2*n)/2.

Original entry on oeis.org

1, 5, 22, 91, 369, 1486, 5962, 23884, 95607, 382568, 1530552, 6122765, 24492171, 97970902, 391888040, 1567561019, 6270261786, 25081082556, 100324401036, 401297745749, 1605191266193, 6420765631136, 25683063657239, 102732256894319
Offset: 1

Views

Author

Omar E. Pol, Nov 30 2012

Keywords

Links

Crossrefs

Bisection of A093370.
Cf. A093371, A122536, A216955.

Extensions

More terms from Hakan Icoz, Sep 04 2020

A211965 Number of binary sequences of length 2n-1 and curling number 1.

Original entry on oeis.org

2, 4, 12, 40, 148, 572, 2248, 8920, 35536, 141860, 566880, 2266400, 9063372, 36249044, 144987304, 579931488, 2319690516, 9278691224, 37114623248, 148458209744, 593832272556, 2375327957436, 9501309564288, 38005233726372, 152020925844036
Offset: 1

Views

Author

Omar E. Pol, Nov 28 2012

Keywords

Comments

Equivalently, number of binary sequences of length 2n-1 with no initial repeats (see A122536).

Links

Crossrefs

Bisection of A122536.
Cf. A093371, A211966, A216955, A216958.

Formula

a(n) = 2*A093371(2n-1).
a(n) = 2*A211966(n-1), n >= 2.

A211966 Number of binary sequences of length 2n and curling number 1.

Original entry on oeis.org

2, 6, 20, 74, 286, 1124, 4460, 17768, 70930, 283440, 1133200, 4531686, 18124522, 72493652, 289965744, 1159845258, 4639345612, 18557311624, 74229104872, 296916136278, 1187663978718, 4750654782144, 19002616863186, 76010462922018
Offset: 1

Views

Author

Omar E. Pol, Nov 28 2012

Keywords

Comments

Equivalently, number of binary sequences of length 2n with no initial repeats (see A122536).

Links

Crossrefs

Bisection of A122536.
Cf. A093371, A211965, A216955, A216958.

Formula

a(n) = 2*A093371(2n) = A093371(2n+1) = A211965(n+1)/2.

A216956 Triangle read by rows: A216955/2.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 6, 6, 2, 1, 1, 10, 13, 5, 2, 1, 1, 20, 26, 10, 4, 2, 1, 1, 37, 55, 19, 9, 4, 2, 1, 1, 74, 107, 41, 18, 8, 4, 2, 1, 1, 143, 219, 82, 35, 17, 8, 4, 2, 1, 1, 286, 438, 164, 70, 34, 16, 8, 4, 2, 1, 1, 562, 881, 330, 143, 67, 33, 16, 8, 4, 2, 1, 1, 1124, 1762, 660, 286, 134, 66, 32, 16, 8, 4, 2, 1, 1
Offset: 1

Views

Author

N. J. A. Sloane, Sep 26 2012

Keywords

Comments

It appears that reversed rows converge to A011782. - Omar E. Pol, Nov 20 2012

Examples

			Triangle begins:
1,
1, 1,
2, 1, 1,
3, 3, 1, 1,
6, 6, 2, 1, 1,
10, 13, 5, 2, 1, 1,
20, 26, 10, 4, 2, 1, 1,
37, 55, 19, 9, 4, 2, 1, 1,
74, 107, 41, 18, 8, 4, 2, 1, 1,
...

Links

Crossrefs

First column is A093371.
Cf. A216955.

A211975 A122536(2n)/2.

Original entry on oeis.org

1, 3, 10, 37, 143, 562, 2230, 8884, 35465, 141720, 566600, 2265843, 9062261, 36246826, 144982872, 579922629, 2319672806, 9278655812, 37114552436, 148458068139, 593831989359, 2375327391072, 9501308431593, 38005231461009, 152020921313377
Offset: 1

Views

Author

Omar E. Pol, Nov 30 2012

Keywords

Links

Crossrefs

Bisection of A093371.
Cf. A093370, A121880, A216955.
Previous Showing 11-17 of 17 results.

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

Content is available under The OEIS End-User License Agreement.