A288706 Number of (undirected) paths in the n-sun graph.
108, 614, 3840, 26937, 211722, 1852300, 17900118, 189670655, 2188938928, 27349969842, 368010246500, 5307501200421, 81699366763710, 1337244268935960, 23195236251394954, 425069874742963563, 8207267847726907028, 166543057722717660670, 3543666872978746093608, 78898851731990085876113
Offset: 3
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 3..200
- Andrew Howroyd, Derivation of formula, Jun 2025.
- Eric Weisstein's World of Mathematics, Graph Path.
- Eric Weisstein's World of Mathematics, Sun Graph.
Crossrefs
Cf. A234627.
Programs
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PARI
a(n) = {my(s=sum(k=1, n, sum(i=0, min(k,n-k), binomial(k,i)*binomial(n-1,k+i-1)*2^i*(k-1)!*((5*k-2*i) - n*i/(k+i) + if(k>1, (i*(i+3) + 4*k*(k-1-i))/(k-1)))/k))); (2*(n-1) - 1 + s)*n/2} \\ Andrew Howroyd, Jun 17 2025
Extensions
a(10) from Eric W. Weisstein, Sep 09 2017
a(11)-a(12) from Eric W. Weisstein, Mar 14 2019
a(13) onwards from Andrew Howroyd, Jun 17 2025