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 A270227 Array read by antidiagonals: T(n,m) = number of matchings (i.e., Hosoya index) in K_n X K_m. 8
 1, 2, 2, 4, 7, 4, 10, 32, 32, 10, 26, 193, 370, 193, 26, 76, 1382, 5950, 5950, 1382, 76, 232, 11719, 122984, 270529, 122984, 11719, 232, 764, 112604, 3175696, 16873930, 16873930, 3175696, 112604, 764, 2620, 1221889, 98815588, 1384880065, 3337807996, 1384880065, 98815588, 1221889, 2620 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Observations: (for n+m <= 32) Examination of values modulus a small prime yields several patterns. T(n,m) == (n+1)*(m+1) (mod 2) for n+m>2. T(n,m) == T(n,m+6) (mod 3). T(n,m) is not divisible by 3. T(n,m) == 0 (mod 5) for n==4 (mod 5) and m<>2 and except when m=n=4. T(5,m) == 0 (mod 208) for m >= 13. T(6,m) == 0 (mod 19) for m >= 19. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..496 Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Rook Graph EXAMPLE The start of the sequence as table: * 1 2 4 10 26 76 ... * 2 7 32 193 1382 11719 ... * 4 32 370 5950 122984 3175696 ... * 10 193 5950 270529 16873930 1384880065 ... * 26 1382 122984 168739305 3337807996 909046586596 ... * 76 11719 3175696 1384880065 909046586596 855404716021831 ... * ... CROSSREFS Main diagonal is A270228. Rows include A000085, A270229. Sequence in context: A347940 A208269 A184761 * A162251 A244011 A065968 Adjacent sequences: A270224 A270225 A270226 * A270228 A270229 A270230 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Mar 13 2016 STATUS approved

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Last modified December 5 01:00 EST 2023. Contains 367565 sequences. (Running on oeis4.)