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A253678 Number of perfect matchings in the graph C_8 X C_n. 8
1058, 39952, 155682, 3113860, 19681538, 311853312, 2415542018, 33898728836, 294554220578, 3827188349968, 35866638601250, 442299574618756, 4365923647238658, 51942700201804032, 531410627302657538, 6169093269471927940, 64681086501382749218, 738453913359765339152, 7872683691901209561122, 88873260229652630182276 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

S. N. Perepechko, Combinatorial properties of dimer problem on tori (in Russian). Mathematical physics and its applications, The fourth int. conf. Samara, 2014, 280-281.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 3..500

Eric Weisstein's World of Mathematics, Independent Edge Set

Eric Weisstein's World of Mathematics, Matching

Eric Weisstein's World of Mathematics, Perfect Matching

Eric Weisstein's World of Mathematics, Torus Grid Graph

FORMULA

a(n) = 14*a(n-1) + 145*a(n-2) - 2492*a(n-3) - 5832*a(n-4) + 164332*a(n-5) + 6360*a(n-6) - 5592188*a(n-7) + 5575094*a(n-8) + 111829704*a(n-9) - 176471286*a(n-10) - 1404071060*a(n-11) + 2757391176*a(n-12) + 11493707876*a(n-13) - 26094214040*a(n-14) - 62666476628*a(n-15) + 161092194209*a(n-16) + 229194775110*a(n-17) - 673504262865*a(n-18) - 556186915928*a(n-19) + 1946775340976*a(n-20) + 855365272888*a(n-21) - 3933950269712*a(n-22) - 705783359960*a(n-23) + 5586898052980*a(n-24) - 5586898052980*a(n-26) + 705783359960*a(n-27) + 3933950269712*a(n-28) - 855365272888*a(n-29) - 1946775340976*a(n-30) + 556186915928*a(n-31) + 673504262865*a(n-32) - 229194775110*a(n-33) - 161092194209*a(n-34) + 62666476628*a(n-35) + 26094214040*a(n-36) - 11493707876*a(n-37) - 2757391176*a(n-38) + 1404071060*a(n-39) + 176471286*a(n-40) - 111829704*a(n-41) - 5575094*a(n-42) + 5592188*a(n-43) - 6360*a(n-44) - 164332*a(n-45) + 5832*a(n-46) + 2492*a(n-47) - 145*a(n-48) - 14*a(n-49) + a(n-50).

G.f.: 2*x^3*(529 + 12570*x - 278528*x^2 - 1111096*x^3 + 29622124*x^4 + 15949216*x^5 - 1354335880*x^6 + 1073870160*x^7 + 33231636934*x^8 - 49093408612*x^9 - 484852497568*x^10 + 922702092728*x^11 + 4448623050276*x^12 - 9889298009728*x^13 - 26519860399096*x^14 + 66909591407824*x^15 + 104242913448099*x^16 - 300153880511538*x^17 - 268804327853184*x^18 + 917127529551440*x^19 + 437177534552376*x^20 - 1937370697752896*x^21 - 386856893695952*x^22 + 2851262465341600*x^23 + 31463729114724*x^24 - 2933939639544920*x^25 + 353114911609152*x^26 + 2113468417316080*x^27 - 452714140134072*x^28 - 1064902306141568*x^29 + 302352881352848*x^30 + 373692292484128*x^31 - 126783009087417*x^32 - 90391126093930*x^33 + 35100066280832*x^34 + 14772327002472*x^35 - 6497628908516*x^36 - 1572040067936*x^37 + 799287715544*x^38 + 101192826896*x^39 - 63992712074*x^40 - 3215530756*x^41 + 3212411488*x^42 - 3162664*x^43 - 94666796*x^44 + 3355392*x^45 + 1438440*x^46 - 83696*x^47 - 8091*x^48 + 578*x^49)/((1-x)*(1+x)*(1+4*x+x^2)*(1-4*x+x^2)*(1-2*x-x^2)*(1+2*x-x^2)*(1+8*x+16*x^2+8*x^3+x^4)* (1-14*x+34*x^2-14*x^3+x^4)*(1-8*x+16*x^2-8*x^3+x^4)*(1-4*x^2+x^4)*(1+4*x-4*x^2-4*x^3+x^4)*(1+8*x-10*x^2-8*x^3+x^4)*(1-4*x-4*x^2+4*x^3+x^4)*(1-8*x-10*x^2+8*x^3+x^4)*(1-14*x^2+34*x^4-14*x^6+x^8)).

CROSSREFS

Row n=4 of A341741.

Cf. A231087, A220864, A231485, A232804, A230033.

Sequence in context: A035858 A120215 A202611 * A035760 A107556 A237797

Adjacent sequences:  A253675 A253676 A253677 * A253679 A253680 A253681

KEYWORD

nonn,changed

AUTHOR

Sergey Perepechko, Jan 09 2015

STATUS

approved

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Last modified March 3 04:02 EST 2021. Contains 341756 sequences. (Running on oeis4.)