A308350 Number of maximum irredundant sets in the n-web graph.
21, 24, 135, 16, 448, 96, 1620, 64, 4400, 384, 13104, 256, 32640, 1536, 88128, 1024, 209152, 6144, 532224, 4096, 1224704, 24576, 2995200, 16384, 6746112, 98304, 16035840, 65536, 35553280, 393216, 82722816, 262144, 181207040, 1572864, 414646272, 1048576, 899678208, 6291456
Offset: 3
Links
- Andrew Howroyd, Table of n, a(n) for n = 3..1000
- Eric Weisstein's World of Mathematics, Maximum Irredundant Vertex Set.
- Eric Weisstein's World of Mathematics, Web Graph.
- Index entries for linear recurrences with constant coefficients, signature (0,2,0,8,0,-16,0,-16,0,32).
Programs
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PARI
a(n)={my(m=n\4); 4^m*if(n%2, if(n%4==1, 9*(4*m + 1)*(2*m + 1)/4, (4*m + 3)*(9*m + 7)), if(n%4==0, 6, 4))} \\ Andrew Howroyd, May 28 2025
Formula
From Andrew Howroyd, May 28 2025: (Start)
G.f.: x^3*(21 + 24*x + 93*x^2 - 32*x^3 + 10*x^4 - 128*x^5 - 20*x^6 + 128*x^7 + 72*x^8 + 128*x^9)/((1 - 2*x^2)^3*(1 + 2*x^4)^2).
a(4*n) = 6*4^n; a(4*n+1) = 9*(4*n + 1)*(2*n + 1)*4^(n-1); a(4*n+2) = 4*4^n; a(4*n+3) = (4*n + 3)*(9*n + 7)*4^n. (End)
Extensions
a(10) from Eric W. Weisstein, Jun 10 2021
a(11) onwards from Andrew Howroyd, May 28 2025