A143941 The Wiener index of a chain of n triangles (i.e., joined like VVV..VV; here V is a triangle!).
3, 14, 37, 76, 135, 218, 329, 472, 651, 870, 1133, 1444, 1807, 2226, 2705, 3248, 3859, 4542, 5301, 6140, 7063, 8074, 9177, 10376, 11675, 13078, 14589, 16212, 17951, 19810, 21793, 23904, 26147, 28526, 31045, 33708, 36519, 39482, 42601, 45880, 49323, 52934
Offset: 1
Examples
a(2)=14 because in the graph VV (V is a triangle!) we have 6 distances equal to 1 and 4 distances equal to 2.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Eric Weisstein's World of Mathematics, Bishop Graph
- Eric Weisstein's World of Mathematics, Circuit Rank
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
[n*(1+6*n+2*n^2)/3 : n in [1..40]]; // Wesley Ivan Hurt, Apr 08 2015
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Maple
seq((1/3)*n*(1+6*n+2*n^2), n=1..43);
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Mathematica
CoefficientList[Series[(3+2*x-x^2)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jul 03 2012 *) LinearRecurrence[{4,-6,4,-1},{3,14,37,76},50] (* Harvey P. Dale, Sep 06 2023 *)
Formula
a(n) = n*(1 + 6*n + 2*n^2)/3.
G.f.: z*(3 + 2*z - z^2)/(1-z)^4.
a(n) = Sum_{k=1..n} k*A143940(n,k).
a(n) = Sum_{k=1..n} A142463(k). - Richard R. Forberg, Jan 09 2015
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, Apr 08 2015
E.g.f.: exp(x)*x*(9 + 12*x + 2*x^2)/3. - Stefano Spezia, Jan 03 2022
Comments