Search: id:A122023
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%I A122023
%S A122023 0,1,3,11,29,109,283,795,2061,5053,13099,30091,78013,173453,449723,
%T A122023 983163,2549229,5523677,14322635,30887915,80092061,172288429,446745691,
%U A122023 959703003,2488530381,5341975549,13851888235,29723290699,77073397885
%N A122023 Vacuum Virtual Particle 10 vertex graph as Feynman diagram seen as a 
               10 X 10 bonding graph vector Matrix Markov: characteristic Polynomial: 
               x^4(-3 + x^2)(8 - 7 x^2 + x^4).
%C A122023 Calculation of relative energy of ten particle states as secular equation: 
               aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[10]] == 0, x][[n]], 
               {n, 1, 10}] Sum[2*aaa[[n]], {n, 1, 5}]=-10.5794 The excess energy 
               is about 8*alpha if each vertex is taken as one unit.
%F A122023 M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, 
               {0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 
               0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 
               0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 
               0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}} v[1] = Table[Fibonacci[n], 
               {n, 0, 9}] v[n_] := v[n] = M.v[n - 1] a(n) = v[n][[1]]
%t A122023 M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {1, 0, 1, 1, 0, 0, 0, 0, 0, 0}, 
               {0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 
               0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 1, 0, 0, 0}, {0, 0, 
               0, 0, 1, 1, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 
               0, 0, 0, 1, 1, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}} v[1] = Table[Fibonacci[n], 
               {n, 0, 9}] v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], 
               {n, 1, 50}]
%Y A122023 Sequence in context: A110954 A000251 A159229 this_sequence A009183 A165893 
               A106397
%Y A122023 Adjacent sequences: A122020 A122021 A122022 this_sequence A122024 A122025 
               A122026
%K A122023 nonn,uned
%O A122023 1,3
%A A122023 Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 12 2006

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