A231829 -id:A231829 - cp's OEIS frontend

A339118 Number of cycles in the grid graph P_6 X P_n.

15, 275, 5034, 80626, 1222363, 18438929, 279285399, 4237530095, 64300829449, 975566486675, 14800469958185, 224540402345213, 3406558215857382, 51681816786790684, 784078741397570677, 11895467318139343215, 180469294422664219486, 2737947622842077799930

Offset: 2

Seiichi Manyama, Nov 24 2020

nonn

Andrew Howroyd, Table of n, a(n) for n = 2..500
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Cf. A140517, A145401, A231829.

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
def A339118(n):
    return A(6, n)
print([A339118(n) for n in range(2, 13)])

Empirical g.f.: -x^2 * (15 - 325*x + 3889*x^2 - 32204*x^3 + 166496*x^4 - 439661*x^5 + 117553*x^6 + 2506529*x^7 - 5691052*x^8 - 128310*x^9 + 16209330*x^10 - 15148184*x^11 - 17089827*x^12 + 28709449*x^13 + 11141815*x^14 - 27136640*x^15 - 13792528*x^16 + 20876587*x^17 + 15963209*x^18 - 11646759*x^19 - 10681356*x^20 + 3192142*x^21 + 3419602*x^22 - 252986*x^23 - 401310*x^24 - 43774*x^25 + 13852*x^26 + 2950*x^27 - 278*x^28 - 48*x^29 + 4*x^30) / ((-1 + x)^2 * (-1 + 38*x - 580*x^2 + 4945*x^3 - 26274*x^4 + 84913*x^5 - 122213*x^6 - 183068*x^7 + 1124479*x^8 - 1544617*x^9 - 1129508*x^10 + 5346947*x^11 - 3023145*x^12 - 6147688*x^13 + 6904233*x^14 + 3952819*x^15 - 5690282*x^16 - 4144167*x^17 + 3164355*x^18 + 4915006*x^19 - 1267655*x^20 - 3336331*x^21 + 82962*x^22 + 1051157*x^23 + 93428*x^24 - 119962*x^25 - 23089*x^26 + 2688*x^27 + 1368*x^28 - 34*x^29 - 30*x^30 + 2*x^31)). - Vaclav Kotesovec, Dec 09 2020

Terms a(13) and beyond from Andrew Howroyd, Dec 08 2020

A339119 Number of cycles in the grid graph P_7 X P_n.

Original entry on oeis.org

21, 681, 23984, 692194, 18438929, 487150371, 12947640143, 345142437669, 9203308475041, 245355064111139, 6540331954247241, 174341025325354201, 4647322411026104632, 123881845810609904802, 3302270967098053652763, 88027348826922694314763, 2346510376337057464408514

Offset: 2

Seiichi Manyama, Nov 24 2020

nonn

a(n+1) / a(n) tends to 26.65660630533835653493851570574867751479178653672292060740586256111131858... - Vaclav Kotesovec, Nov 24 2020

Seiichi Manyama, Table of n, a(n) for n = 2..500
Vaclav Kotesovec, Empirical g.f.
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Cf. A140517, A231829.

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
def A339119(n):
    return A(n, 7)
print([A339119(n) for n in range(2, 15)])

A339120 Number of cycles in the grid graph P_8 X P_n.

Original entry on oeis.org

28, 1664, 114069, 5948291, 279285399, 12947640143, 603841648931, 28251882697663, 1322310119854705, 61875355046353061, 2895006802805407868, 135448608195945754204, 6337277838067727854392, 296505504331623399871908, 13872765058478362509835979, 649072483984291902586660423

Offset: 2

Seiichi Manyama, Nov 24 2020

nonn

Andrew Howroyd, Table of n, a(n) for n = 2..200
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Cf. A140517, A145418, A231829.

Terms a(10) and beyond from Andrew Howroyd, Dec 08 2020

A339121 Number of cycles in the grid graph P_9 X P_n.

Original entry on oeis.org

36, 4040, 542295, 51139577, 4237530095, 345142437669, 28251882697663, 2318527339461265, 190273063549680295, 15609156135669687673, 1280305089790914190288, 105011610206669201362004, 8613171107463963712000106, 706463610718638922253288622, 57945052730138702492774189915

Offset: 2

Seiichi Manyama, Nov 24 2020

nonn

Seiichi Manyama, Table of n, a(n) for n = 2..150
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Cf. A140517, A231829.

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
def A339121(n):
    return A(n, 9)
print([A339121(n) for n in range(2, 15)])

A358785 Number of cycles in the grid graph P_11 X P_n.

Original entry on oeis.org

55, 23637, 12253948, 3779989098, 975566486675, 245355064111139, 61875355046353061, 15609156135669687673, 3931128009418993765997, 988808811046283595068099, 248581947999911644069460438, 62479777983071973470513443588, 15702642238437709110690166048520

Offset: 2

Seiichi Manyama, Nov 30 2022

nonn

Seiichi Manyama, Table of n, a(n) for n = 2..40
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Row 10 of A231829.

A358707 Number of cycles in the grid graph P_10 X P_n.

Original entry on oeis.org

45, 9779, 2577870, 439673502, 64300829449, 9203308475041, 1322310119854705, 190273063549680295, 27359264067916806101, 3931128009418993765997, 564680431992866012642342, 81106350080343571152166324, 11649258590678717543578165244, 1673159830616398545304368383554

Offset: 2

Seiichi Manyama, Nov 30 2022

nonn

Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph

Row 9 of A231829.

Cf. A140517.

a(12)-a(15) from Andrew Howroyd, Jan 28 2023

cp's OEIS Frontend

A339118 Number of cycles in the grid graph P_6 X P_n.

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A339119 Number of cycles in the grid graph P_7 X P_n.

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A339120 Number of cycles in the grid graph P_8 X P_n.

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A339121 Number of cycles in the grid graph P_9 X P_n.

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A358785 Number of cycles in the grid graph P_11 X P_n.

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A358707 Number of cycles in the grid graph P_10 X P_n.

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