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 A086113 Number of 3 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing. 11
 6, 36, 102, 216, 390, 636, 966, 1392, 1926, 2580, 3366, 4296, 5382, 6636, 8070, 9696, 11526, 13572, 15846, 18360, 21126, 24156, 27462, 31056, 34950, 39156, 43686, 48552, 53766, 59340, 65286, 71616, 78342, 85476, 93030, 101016, 109446, 118332 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March challenge Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 2*n*(n^2 + 3*n - 1) = 2*n*A014209(n). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m-1, n)-m) = 2*m*(2*binomial(m+n-1, m)-n). G.f.: 6*x*(1 + 2*x - x^2)/(1-x)^4. - Vincenzo Librandi, Jun 24 2012 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 24 2012 MATHEMATICA CoefficientList[Series[6*(1+2x-x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 24 2012 *) PROG (MAGMA) I:=[6, 36, 102, 216]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 24 2012 CROSSREFS Cf. A032260, A016742, A086114, A086115. Sequence in context: A207392 A207939 A207462 * A207903 A267714 A207747 Adjacent sequences:  A086110 A086111 A086112 * A086114 A086115 A086116 KEYWORD nonn,easy AUTHOR Vladimir Baltic, Vladeta Jovovic, Jul 10 2003 STATUS approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)