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 A192839 Molecular topological indices of the square graphs. 1
 0, 48, 768, 4320, 15360, 42000, 96768, 197568, 368640, 641520, 1056000, 1661088, 2515968, 3690960, 5268480, 7344000, 10027008, 13441968, 17729280, 23046240, 29568000, 37488528, 47021568, 58401600, 71884800, 87750000, 106299648, 127860768, 152785920, 181454160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 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) = 8*n*(n+1)*(n-1)^3. G.f.: 48*x^2*(1+x)*(1+9*x)/(1-x)^6. - Colin Barker, Aug 07 2012 E.g.f.: 8*x^2*(3 + 13*x + 8*x^2 + x^3)*exp(x). - G. C. Greubel, Jan 04 2019 From Amiram Eldar, Apr 16 2022: (Start) Sum_{n>=2} 1/a(n) = 13/128 - Pi^2/64 + zeta(3)/16. Sum_{n>=2} (-1)^n/a(n) = log(2)/4 - Pi^2/128 - 17/128 + 3*zeta(3)/64. (End) MAPLE [8*n*(n+1)*(n-1)^3\$n=1..30]; # Muniru A Asiru, Jan 05 2019 MATHEMATICA Table[, {n, 1, 30}] (* G. C. Greubel, Jan 04 2019 *) PROG (PARI) vector(30, n, 8*n*(n+1)*(n-1)^3) \\ G. C. Greubel, Jan 04 2019 (Magma) [8*n*(n+1)*(n-1)^3: n in [1..30]]; // G. C. Greubel, Jan 04 2019 (Sage) [8*n*(n+1)*(n-1)^3 for n in (1..30)] # G. C. Greubel, Jan 04 2019 (GAP) List([1..30], n -> 8*n*(n+1)*(n-1)^3); # G. C. Greubel, Jan 04 2019 CROSSREFS Sequence in context: A145155 A105948 A350378 * A014401 A241873 A233784 Adjacent sequences: A192836 A192837 A192838 * A192840 A192841 A192842 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Jul 11 2011 STATUS approved

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