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A277977 a(n) = n*(1-3n+2*n^2+2*n^3)/2. 0

%I

%S 0,1,19,96,298,715,1461,2674,4516,7173,10855,15796,22254,30511,40873,

%T 53670,69256,88009,110331,136648,167410,203091,244189,291226,344748,

%U 405325,473551,550044,635446,730423,835665,951886,1079824,1220241,1373923,1541680,1724346

%N a(n) = n*(1-3n+2*n^2+2*n^3)/2.

%C For n>=3, a(n) is the second Zagreb index of the graph obtained by joining one vertex of a complete graph K[n] with each vertex of a second complete graph K[n].

%C 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.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: x*(1+x)*(1+13*x-2*x^2)/(1-x)^5. - _Robert Israel_, Nov 07 2016

%e a(4) = 298. Indeed, the corresponding graph has 16 edges. We list the degrees of their endpoints: (3,3), (3,3), (3,3), (3,7), (3,7), (3,7), (4,4), (4,4), (4,4), (4,4), (4,4), (4,4), (4,7), (4,7), (4,7), (4,7). Then, the second Zagreb index is 3*9 + 3*21 + 6*16 + 4*28 = 298.

%p seq((1/2)*n*(1-3*n+2*n^2+2*n^3), n = 0 .. 45);

%o (PARI) a(n) = n*(1-3*n+2*n^2+2*n^3)/2 \\ _Felix Fröhlich_, Nov 07 2016

%o (PARI) concat(0, Vec(x*(1+x)*(1+13*x-2*x^2)/(1-x)^5 + O(x^40))) \\ _Felix Fröhlich_, Nov 07 2016

%Y Cf. A213820.

%K nonn

%O 0,3

%A _Emeric Deutsch_, Nov 07 2016

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.