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Search: a005551 -id:a005551
Displaying 1-7 of 7 results found. page 1
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A003289 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,1).
(Formerly M1229) 		+10
8
1, 2, 4, 10, 30, 98, 328, 1140, 4040, 14542, 53060, 195624, 727790, 2728450, 10296720, 39084190, 149115456, 571504686, 2199310460, 8494701152, 32919635606, 127961125094, 498775164568, 1949112527750, 7634623480172 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=1..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Equals A001335(n+1) / 6 for n > 1.
Cf. A003290, A003291, A005549, A005550, A005551, A005552, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 13 2016
a(23)-a(24) from Bert Dobbelaere, Jan 03 2019
a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A003290 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,2).
(Formerly M4119) 		+10
7
1, 6, 18, 50, 156, 508, 1724, 6018, 21440, 77632, 284706, 1055162, 3944956, 14858934, 56325420, 214698578, 822373244, 3163606784, 12217121138, 47343356398, 184038696776, 717456797490, 2804219712064, 10986639618642 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=2..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003291, A005549, A005550, A005551, A005552, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 13 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A003291 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,1).
(Formerly M1613) 		+10
7
2, 6, 16, 46, 140, 464, 1580, 5538, 19804, 71884, 264204, 980778, 3671652, 13843808, 52519836, 200320878, 767688176, 2954410484, 11412815256, 44237340702, 171997272012, 670612394118, 2621415708492, 10271274034254 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=2..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003290, A005549, A005550, A005551, A005552, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 14 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A005549 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (0,3).
(Formerly M4842) 		+10
7
1, 12, 54, 188, 636, 2168, 7556, 26826, 96724, 353390, 1305126, 4864450, 18272804, 69103526, 262871644, 1005137688, 3860909698, 14890903690, 57641869140, 223864731680, 872028568182, 3406103773674, 13337263822236 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=3..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003290, A003291, A005550, A005551, A005552, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and improved title from Sean A. Irvine, Feb 14 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A005550 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,2).
(Formerly M3012) 		+10
7
3, 16, 57, 184, 601, 2036, 7072, 25088, 90503, 330836, 1222783, 4561058, 17145990, 64888020, 246995400, 944986464, 3631770111, 14013725268, 54268946152, 210842757798, 821569514032, 3209925357702, 12572219405144 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=3..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003290, A003291, A005549, A005551, A005552, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 15 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A005552 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (1,3).
(Formerly M3657) 		+10
7
4, 35, 166, 633, 2276, 8107, 29086, 105460, 386320, 1428664, 5327738, 20014741, 75677726, 287784832, 1099944240, 4223170456, 16280541834, 62992268833, 244536402984, 952154191644, 3717618386556, 14551788319328 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=4..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003290, A003291, A005549, A005550, A005551, A005553.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 15 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
A005553 Number of n-step self-avoiding walks on hexagonal lattice from (0,0) to (2,2).
(Formerly M4235) 		+10
7
6, 40, 174, 644, 2268, 8020, 28666, 103696, 379450, 1402276, 5227366, 19633732, 74230146, 282273744, 1078902168, 4142578832, 15970882784, 61798680076, 239921541412, 934258870200, 3648030627298, 14280474288676 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Table of n, a(n) for n=4..25.
D. S. McKenzie, The end-to-end length distribution of self-avoiding walks, J. Phys. A 6 (1973), 338-352.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
CROSSREFS
Cf. A001335, A003289, A003290, A003291, A005549, A005550, A005551, A005552.
KEYWORD
nonn,walk,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms and title improved by Sean A. Irvine, Feb 15 2016
a(23)-a(25) from Bert Dobbelaere, Jan 15 2019
STATUS
approved
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Last modified August 29 23:09 EDT 2024. Contains 375519 sequences. (Running on oeis4.)