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 11-14 of 14 results.

A231888 Number of maximal 3-independent sets in the 3-dimensional (3, 3, n) grid graph.

Original entry on oeis.org

0, 7, 26, 57, 190, 646, 1914, 5960, 18824, 58248, 181196, 565328, 1759720, 5477376, 17062956, 53131824, 165443096, 515219344, 1604410136, 4996129756, 15558217340, 48448930636, 150871392396, 469819443204, 1463035474136, 4555944690588, 14187380873768
Offset: 0

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Crossrefs

Extensions

Terms a(13) and beyond from Andrew Howroyd, Jun 10 2017

A197053 Number of nX7 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.

Original entry on oeis.org

7, 26, 156, 692, 3580, 17742, 88056, 439338, 2192602, 10912392, 54394628, 271160024, 1351103246, 6733077562, 33557756016, 167232569172, 833404135538, 4153405692526, 20698773896328, 103153449929238, 514074952403758
Offset: 1

Views

Author

R. H. Hardin Oct 09 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's
Column 7 of A197054

Examples

			Some solutions for n=4
..0..2..1..0..1..2..0....0..1..1..1..0..3..0....0..2..0..3..0..3..0
..3..0..2..1..2..0..3....1..2..0..1..3..0..2....1..1..2..0..4..0..3
..0..4..0..3..0..4..0....2..0..3..1..0..2..1....2..0..2..2..0..4..0
..2..0..3..0..3..0..2....0..3..0..1..1..1..0....0..3..0..1..2..0..2
		

Formula

Empirical: a(n) = 2*a(n-1) +9*a(n-2) +37*a(n-3) -187*a(n-5) -77*a(n-6) +248*a(n-7) +240*a(n-8) -1400*a(n-9) +564*a(n-10) +1220*a(n-11) +1358*a(n-12) -5000*a(n-13) +3019*a(n-14) +1209*a(n-15) +4104*a(n-16) -6840*a(n-17) +3995*a(n-18) +4214*a(n-19) -1497*a(n-20) -1140*a(n-21) -945*a(n-22) +1251*a(n-23) -2502*a(n-24) -60*a(n-25) -49*a(n-26) -272*a(n-27) +281*a(n-28) -376*a(n-29) -109*a(n-30) +103*a(n-31) +9*a(n-32) -27*a(n-33) -3*a(n-34) +6*a(n-35)

A231882 Number of maximal 2-independent sets in the planar 3 X n grid graph.

Original entry on oeis.org

0, 3, 4, 11, 17, 36, 69, 133, 254, 499, 959, 1852, 3589, 6943, 13410, 25951, 50197, 97050, 187699, 363047, 702066, 1357755, 2625947, 5078438, 9821417, 18994465, 36734648, 71043261, 137395463, 265718350, 513889567, 993844901, 1922062694, 3717202293, 7188941039
Offset: 0

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Crossrefs

Programs

  • Mathematica
    LinearRecurrence[{1,0,3,1,0,1,-2,0,-1},{0,3,4,11,17,36,69,133,254,499},40] (* Harvey P. Dale, Oct 05 2017 *)

Formula

Euler et al. give an explicit g.f. and recurrence.
G.f.: x*(3 + x + 7*x^2 - 3*x^3 + 4*x^4 - 4*x^5 - x^6 - 2*x^7 - x^8) / ((1 + x)*(1 - 2*x + 2*x^2 - 5*x^3 + 4*x^4 - 4*x^5 + 3*x^6 - x^7 + x^8)). - Colin Barker, Oct 03 2017

Extensions

Terms a(10) and beyond from Andrew Howroyd, Jun 10 2017

A293177 Triangle read by rows: T(m,n) = number of maximal independent sets in m X n rectangular grid graph (m>=1, 1<=n<=m).

Original entry on oeis.org

1, 2, 2, 2, 4, 10, 3, 6, 18, 42, 4, 10, 38, 108, 358, 5, 16, 78, 274, 1132, 4468, 7, 26, 156, 692, 3580, 17742, 88056, 9, 42, 320, 1754, 11382, 70616, 439338, 2745186, 12, 68, 654, 4442, 36270, 281202, 2192602, 17155374, 16, 110, 1326, 11248, 114992, 1117442, 10912392, 106972582
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2017

Keywords

Examples

			Triangle begins:
1,
2,2,
2,4,10,
3,6,18,42,
4,10,38,108,358,
5,16,78,274,1132,4468,
7,26,156,692,3580,17742,88056,
9,42,320,1754,11382,70616,439338,2745186,
12,68,654,4442,36270,281202,2192602,17155374,
16,110,1326,11248,114992,1117442,10912392,106972582,
...
		

Crossrefs

Main diagonal is A197048.
Rows 3,4,5,6,... form the beginnings of A197049, A197050, A197051, A197052, ..., respectively.
Triangular version of A197054.
Previous Showing 11-14 of 14 results.