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 A143940 Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in a linear chain of n triangles (i.e., joined like VVV..VV; here V is a triangle!), 1 <= k <= n. 1
 3, 6, 4, 9, 8, 4, 12, 12, 8, 4, 15, 16, 12, 8, 4, 18, 20, 16, 12, 8, 4, 21, 24, 20, 16, 12, 8, 4, 24, 28, 24, 20, 16, 12, 8, 4, 27, 32, 28, 24, 20, 16, 12, 8, 4, 30, 36, 32, 28, 24, 20, 16, 12, 8, 4, 33, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 36, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The entries in row n are the coefficients of the Wiener polynomial of a linear chain of n triangles. Sum of entries in row n = n(2n+1) = A014105(n). Sum_{k=1..n} k*T(n,k) = the Wiener index of the linear chain of n triangles = A143941(n). LINKS B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969. FORMULA T(n,1)=3n; T(n,k) = 4(n-k+1) for k>1. G.f. = G(q,z) = qz/(3+qz)/((1-qz)*(1-z)^2). EXAMPLE T(2,1)=6 because the chain of 2 triangles has 6 edges. Triangle starts:    3;    6,  4;    9,  8,  4;   12, 12,  8,  4;   15, 16, 12,  8,  4; MAPLE T:=proc(n, k) if n < k then 0 elif k = 1 then 3*n else 4*n-4*k+4 end if end proc: for n to 12 do seq(T(n, k), k=1..n) end do; # yields sequence in triangular form CROSSREFS Cf. A014105, A143941. Sequence in context: A083682 A021278 A336761 * A321773 A083349 A065230 Adjacent sequences:  A143937 A143938 A143939 * A143941 A143942 A143943 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Sep 06 2008 STATUS approved

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Last modified January 20 10:31 EST 2022. Contains 350471 sequences. (Running on oeis4.)