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 A277108 a(n) = 4n*(n+5). 1
 24, 56, 96, 144, 200, 264, 336, 416, 504, 600, 704, 816, 936, 1064, 1200, 1344, 1496, 1656, 1824, 2000, 2184, 2376, 2576, 2784, 3000, 3224, 3456, 3696, 3944, 4200, 4464, 4736, 5016, 5304, 5600, 5904, 6216, 6536, 6864, 7200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the second Zagreb index of the helm graph H[n] (n>=3). The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g. The M-polynomial of the Helm graph H[n] is M(H[n]; x,y) = n*x*y^4 + n*x^4*y^4 + n*x^4*y^n. - Emeric Deutsch, May 11 2018 The helm graph H[n] is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. - Emeric Deutsch, May 11 2018 a(n) - 16*n + 1 is a square. - Muniru A Asiru, Jun 01 2018 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..5000 E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102. Eric Weisstein's World of Mathematics, Helm Graph Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA G.f.: G(z) = 8z(3-2z)/(1-z)^3. a(n) = 4*A028557(n) = 8*A055998(n). MAPLE seq(4*n^2+20*n, n = 1 .. 40); MATHEMATICA Table[4 n (n + 5), {n, 40}] (* or *) Rest@ CoefficientList[Series[8 x (3 - 2 x)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, Nov 06 2016 *) PROG (PARI) a(n)=4*n*(n+5) \\ Charles R Greathouse IV, Jun 17 2017 (GAP) List([1..50], n->4*n*(n+5)); # Muniru A Asiru, Jun 01 2018 CROSSREFS Cf. A028557, A055998, A132761. Sequence in context: A216697 A332541 A316361 * A039375 A043198 A043978 Adjacent sequences: A277105 A277106 A277107 * A277109 A277110 A277111 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Nov 05 2016 STATUS approved

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Last modified May 18 02:04 EDT 2024. Contains 372615 sequences. (Running on oeis4.)