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 11-13 of 13 results.

A151694 G.f.: Product_{k>=1} (1 + 2*x^(2^k-1) + 2*x^(2^k)).

Original entry on oeis.org

1, 2, 2, 2, 6, 8, 4, 2, 6, 8, 8, 16, 28, 24, 8, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88, 104, 64, 16, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88, 104, 64, 20, 16, 28, 32, 48, 88, 104, 72, 56, 88, 120, 160, 272, 384, 336, 160, 32, 2, 6, 8, 8, 16, 28, 24, 12, 16, 28, 32, 48, 88
Offset: 0

Views

Author

N. J. A. Sloane, Jun 04 2009

Keywords

Examples

			From _Omar E. Pol_, Jun 09 2009: (Start)
Triangle begins:
  1;
  2,2;
  2,6,8,4;
  2,6,8,8,16,28,24,8;
  2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,16;
  2,6,8,8,16,28,24,12,16,28,32,48,88,104,64,20,16,28,32,48,88,104,72,56,88,...
(End)

Links

Crossrefs

For generating functions of the form Product_{k>=c} (1 + a*x^(2^k-1) + b*x^2^k) for the following values of (a,b,c) see: (1,1,0) A160573, (1,1,1) A151552, (1,1,2) A151692, (2,1,0) A151685, (2,1,1) A151691, (1,2,0) A151688 and A152980, (1,2,1) A151550, (2,2,0) A151693, (2,2,1) A151694.
Cf. A000079. - Omar E. Pol, Jun 09 2009

Programs

  • Mathematica
    CoefficientList[Series[Product[1+2x^(2^k-1)+2x^2^k,{k,10}],{x,0,80}],x] (* Harvey P. Dale, Oct 07 2020 *)

A152973 Records in A152968.

Original entry on oeis.org

1, 2, 4, 6, 8, 14, 16, 18, 20, 30, 44, 46, 56, 70, 104, 128, 130, 148, 182, 244, 336, 352, 354, 372, 478, 608, 824, 1024, 1026, 1048, 1054, 1198, 1564, 2040, 2672, 2976, 2978, 3000, 3150, 3960, 5168, 6752, 8320, 8322, 8344, 8348, 8494, 8550, 9306
Offset: 1

Views

Author

Omar E. Pol, Dec 16 2008

Keywords

Comments

Excluding the initial 1, this sequence also gives the records in A151688. - Nathaniel Johnston, Apr 10 2011

Links

Crossrefs

Toothpick structure: A139250.
Cf. A139251, A139252, A152968.
Cf. A152978.

Extensions

More terms from Omar E. Pol, Dec 20 2008
a(17)-a(49) from Nathaniel Johnston, Apr 10 2011

A187214 Number of gulls (or G-toothpicks) added at n-th stage in the first quadrant of the gullwing structure of A187212.

Original entry on oeis.org

0, 1, 1, 2, 2, 4, 5, 4, 2, 4, 6, 6, 8, 14, 15, 8, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 39, 16, 2, 4, 6, 6, 8, 14, 16, 10, 8, 14, 18, 20, 30, 44, 40, 18, 8, 14, 18, 20, 30, 44, 42, 28, 30, 46, 56, 70, 104, 128, 95
Offset: 1

Views

Author

Omar E. Pol, Mar 22 2011, Apr 06 2011

Keywords

Comments

It appears that both a(2) and a(2^k - 1) are odd numbers, for k >= 2. Other terms are even numbers.

Examples

			At stage 1 we start in the first quadrant from a Q-toothpick centered at (1,0) with its endpoints at (0,0) and (1,1). There are no gulls in the structure, so a(1) = 0.
At stage 2 we place a gull (or G-toothpick) with its midpoint at (1,1) and its endpoints at (2,0) and (2,2), so a(2) = 1. There is only one exposed midpoint at (2,2).
At stage 3 we place a gull with its midpoint at (2,2), so a(3) = 1. There are two exposed endpoints.
At stage 4 we place two gulls, so a(4) = 2. There are two exposed endpoints.
At stage 5 we place two gulls, so a(5) = 2. There are four exposed endpoints.
And so on.
If written as a triangle begins:
0,
1,
1,2,
2,4,5,4,
2,4,6,6,8,14,15,8,
2,4,6,6,8,14,16,10,8,14,18,20,30,44,39,16,
2,4,6,6,8,14,16,10,8,14,18,20,30,44,40,18,8,14,18,20,30,44,42,28,...
It appears that rows converge to A151688.

Links

Crossrefs

Cf. A099035, A151550, A151688, A187210, A187211, A187212, A187213, A187220.

Programs

Formula

a(1)=0. a(n) = A187213(n)/2, for n >= 2.
It appears that a(2^k - 1) = A099035(k-1), for k >= 2.
Previous Showing 11-13 of 13 results.

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

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