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 A192832 Molecular topological indices of the lattice graphs. 1
 0, 48, 576, 2880, 9600, 25200, 56448, 112896, 207360, 356400, 580800, 906048, 1362816, 1987440, 2822400, 3916800, 5326848, 7116336, 9357120, 12129600, 15523200, 19636848, 24579456, 30470400, 37440000, 45630000, 55194048, 66298176, 79121280, 93855600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Lattice graphs are defined for n>=2; extended to n=1 using closed form. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Lattice Graph Eric Weisstein's World of Mathematics, Molecular Topological Index Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA a(n) = 4*n^2*(n+1)*(n-1)^2. a(n) = 48*A004302(n). G.f.: 48*x^2*(1+6*x+3*x^2)/(1-x)^6. - Colin Barker, Aug 07 2012 E.g.f.: 4*x^2*(6 +18*x +9*x^2 +x^3)*exp(x). - G. C. Greubel, Jan 04 2019 MATHEMATICA Table[4*n^2*(n+1)*(n-1)^2, {n, 1, 30}] (* G. C. Greubel, Jan 04 2019 *) PROG (PARI) vector(30, n, 4*n^2*(n+1)*(n-1)^2) \\ G. C. Greubel, Jan 04 2019 (Magma) [4*n^2*(n+1)*(n-1)^2: n in [1..30]]; // G. C. Greubel, Jan 04 2019 (Sage) [4*n^2*(n+1)*(n-1)^2 for n in (1..30)] # G. C. Greubel, Jan 04 2019 (GAP) List([0..30], n -> 4*n^2*(n+1)*(n-1)^2); # G. C. Greubel, Jan 04 2019 CROSSREFS Sequence in context: A334713 A266210 A245953 * A352847 A042949 A190601 Adjacent sequences: A192829 A192830 A192831 * A192833 A192834 A192835 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jul 11 2011 STATUS approved

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Last modified April 13 15:06 EDT 2024. Contains 371644 sequences. (Running on oeis4.)