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A145417 Number of 2-factors in P_8 X P_n. 2
0, 13, 27, 2953, 24360, 972080, 13049563, 360783593, 6044482889, 142205412782, 2645920282312, 57787769198498, 1130122135817708, 23838761889677477, 477334902804794530, 9905649696435264827, 200572437515846530901, 4130348948437378850158 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs.

F. Faase, Results from the counting program

FORMULA

Recurrence:

a(1) = 0,

a(2) = 13,

a(3) = 27,

a(4) = 2953,

a(5) = 24360,

a(6) = 972080,

a(7) = 13049563,

a(8) = 360783593,

a(9) = 6044482889,

a(10) = 142205412782,

a(11) = 2645920282312,

a(12) = 57787769198498,

a(13) = 1130122135817708,

a(14) = 23838761889677477,

a(15) = 477334902804794530,

a(16) = 9905649696435264827,

a(17) = 200572437515846530901,

a(18) = 4130348948437378850158,

a(19) = 84074883624291031055071,

a(20) = 1725061733607816846672084,

a(21) = 35201911945083165877105598,

a(22) = 721041937227213471236222936,

a(23) = 14731026760739434523775920272,

a(24) = 301492247130186410656766864436,

a(25) = 6162966556594442193757310209147,

a(26) = 126086101870795129720839096783333,

a(27) = 2578070083185284447937587182277129,

a(28) = 52734387801729163635906223494385644,

a(29) = 1078388240037660942562424414577181926,

a(30) = 22056541466571843558470704997624920958,

a(31) = 451070070689312442562501030339580527821,

a(32) = 9225477593066296020350369342487285559224,

a(33) = 188671988477305551144936342851950180268541,

a(34) = 3858726953408688228729004487413425843715888,

a(35) = 78916582053879579831149431468113368147807393,

a(36) = 1613990623415047770881237325964870382681263773,

a(37) = 33008659899083829723098251801948045543305771504,

a(38) = 675085532254115719882540973806685632932538969963,

a(39) = 13806606434855907791563611600265129790934630275875,

a(40) = 282368982002683765432041412891639191366286828541983,

a(41) = 5774916734695662624117282233886060904936699004411462,

a(42) = 118106924720040350256778966063911938302901243885821967,

a(43) = 2415485198293035324333076932461513145106982243926222725, and

a(n) = 10a(n-1) + 397a(n-2) - 2280a(n-3) - 41718a(n-4) + 171740a(n-5)

+ 1774768a(n-6) - 6621030a(n-7) - 36498440a(n-8) + 142302403a(n-9) + 378226103a(n-10)

- 1722824637a(n-11) - 1841136643a(n-12) + 11820333398a(n-13) + 2592291604a(n-14) - 47333298485a(n-15)

+ 11152811093a(n-16) + 115741226920a(n-17) - 56392421244a(n-18) - 180338596048a(n-19) + 113066783284a(n-20)

+ 185447332605a(n-21) - 129254123956a(n-22) - 129334594126a(n-23) + 92695904156a(n-24) + 62261558431a(n-25)

- 43387609685a(n-26) - 20799137282a(n-27) + 13474013361a(n-28) + 4776521864a(n-29) - 2787760272a(n-30)

- 734922053a(n-31) + 383508601a(n-32) + 72495666a(n-33) - 34918980a(n-34) - 4271202a(n-35)

+ 2078603a(n-36) + 129022a(n-37) - 77626a(n-38) - 773a(n-39) + 1644a(n-40)

- 54a(n-41) - 15a(n-42) + a(n-43).

a(n) = 14*a(n-1) + 331*a(n-2) - 3474*a(n-3) - 24357*a(n-4) + 237534*a(n-5) + 541266*a(n-6) - 6604103*a(n-7) - 1905497*a(n-8) + 85855152*a(n-9) - 60009003*a(n-10) - 545836271*a(n-11) + 672927757*a(n-12) + 1747850343*a(n-13) - 2763674623*a(n-14) - 2917536240*a(n-15) + 5513512152*a(n-16) + 2653029943*a(n-17) - 5852097578*a(n-18) - 1465977019*a(n-19) + 3471750395*a(n-20) + 568784352*a(n-21) - 1167520145*a(n-22) - 154667330*a(n-23) + 221656480*a(n-24) + 23823457*a(n-25) - 24542626*a(n-26) - 1818710*a(n-27) + 1646233*a(n-28) + 57030*a(n-29) - 66339*a(n-30) + 348*a(n-31) + 1479*a(n-32) - 61*a(n-33) - 14*a(n-34) + a(n-35) for n > 35. - Andrew Howroyd, Oct 04 2017

CROSSREFS

Cf. A003693, A222202.

Sequence in context: A018946 A042397 A041336 * A157206 A138685 A047724

Adjacent sequences:  A145414 A145415 A145416 * A145418 A145419 A145420

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 03 2009

EXTENSIONS

Terms a(17) and beyond from Andrew Howroyd, Oct 04 2017

STATUS

approved

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)