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.

Showing 1-2 of 2 results.

A254611 Number of perfect matchings in the P_6 X C_n graph.

Original entry on oeis.org

91, 1681, 2911, 28561, 79808, 591361, 2091817, 13344409, 53924597, 315169009, 1380947751, 7649951296, 35269184041, 188926707649, 899769503723, 4718266032649, 22943942934823, 118691459382721, 584955154102592, 2999832755191441, 14912246613880433, 76049269944443041, 380145205524781061
Offset: 3

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Author

Sergey Perepechko, Feb 02 2015

Keywords

Crossrefs

Formula

G.f. x^3*(91 + 1590*x - 4048*x^2 - 69300*x^3 + 50780*x^4 + 1164101*x^5 - 138254*x^6 - 10058547*x^7 - 1562576*x^8 + 50264529*x^9 + 13812974*x^10 - 155013203*x^11 - 47809304*x^12 + 306988809*x^13 + 89155840*x^14 - 399510007*x^15 - 96791692*x^16 + 345081045*x^17 + 62203726*x^18 - 197547813*x^19 - 23125568*x^20 + 74027795*x^21 + 4550826*x^22 - 17725337*x^23 - 329540*x^24 + 2608475*x^25 - 24182*x^26 - 221705*x^27 + 4727*x^28 + 9737*x^29 - 170*x^30 - 169*x^31)/((1 - x)*(1 + x)*(1 + 3*x - 4*x^2 + x^3)*(1 + 5*x + 6*x^2 + x^3)*(1 - 4*x + 3*x^2 + x^3)*(1 - 2*x - x^2 + x^3)*(1 - x - 2*x^2 + x^3)*(1 - 3*x - 4*x^2 -x^3)*(1 - 6*x + 5*x^2 - x^3)*(1 + 4*x + 3*x^2 - x^3)*(1 + 2*x - x^2 - x^3)*(1 + x - 2*x^2 - x^3)).

A254635 Number of perfect matchings in the P_7 X C_{2n} graph.

Original entry on oeis.org

6272, 179928, 6422528, 248864088, 9973238912, 405583759128, 16603641077888, 681794737794072, 28036464541430912, 1153675328152653912, 47487681076805107712, 1954983080255585201112, 80488830677377147883648, 3313925147228829031300248, 136444682110846678973251712
Offset: 2

Views

Author

Sergey Perepechko, Feb 03 2015

Keywords

Crossrefs

Formula

a(n) = 2*product_{j=1..n} (80 - 98*cos((2*j-1)*Pi/n) + 24*cos(2*(2*j-1)*Pi/n) - 2*cos(3*(2*j-1)*Pi/n)).
G.f.: 8*x^2*(784 - 67669*x + 2453871*x^2 - 50439798*x^3 + 665164698*x^4 - 6023289070*x^5 + 39096248258*x^6 - 187328171158*x^7 + 676655443050*x^8 - 1870967276271*x^9 + 4004062704149*x^10 - 6684136860372*x^11 + 8747997318284*x^12 - 9001233440740*x^13 + 7286680504380*x^14 - 4634602342804*x^15 + 2308061094588*x^16 - 894754403811*x^17 + 267700931657*x^18 - 61077759670*x^19 + 10454781914*x^20 - 1313064750*x^21 + 117311490*x^22 - 7125462*x^23 + 273866*x^24 - 5849*x^25 + 51*x^26)/((1-x)*(1-4*x+x^2)*(1-14*x+34*x^2-14*x^3+x^4)* (1-8*x+16*x^2-8*x^3+x^4) * (1-56*x+672*x^2-2632*x^3+4094*x^4-2632*x^5+672*x^6-56*x^7+x^8)* (1-32*x+288*x^2-928*x^3+1346*x^4-928*x^5+288*x^6-32*x^7+x^8)).
Showing 1-2 of 2 results.