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 A085461 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v5, v2<=v5, v2<=v4 and v3<=v4. 7
 1, 13, 70, 246, 671, 1547, 3164, 5916, 10317, 17017, 26818, 40690, 59787, 85463, 119288, 163064, 218841, 288933, 375934, 482734, 612535, 768867, 955604, 1176980, 1437605, 1742481, 2097018, 2507050, 2978851, 3519151, 4135152, 4834544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of monotone n-weightings of a certain connected bipartite digraph. A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E. KekulĂ© numbers for certain benzenoids. - Emeric Deutsch, Nov 18 2005 Can be constructed by taking the product of the three members of a Pythagorean triples and dividing by 60. Formula: n*(n^2-1)*(n^2+1)/240 where n runs through the odd numbers >= 3. - Pierre Gayet, Apr 04 2009 Number of composable morphisms in a height-n tower of retractions. A retraction between objects X and Y is a pair of maps s:X->Y and r:Y->X such that r(s(x))=x for all x in X. Given objects X_0,X_1,X_2,...,X_n, we can ask for retractions s_i:X_i->X_{i+1},r_i:X_{i+1}->X_i, for each 0<=i

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Last modified January 16 19:49 EST 2019. Contains 319206 sequences. (Running on oeis4.)