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

0, 1, 19, 96, 298, 715, 1461, 2674, 4516, 7173, 10855, 15796, 22254, 30511, 40873, 53670, 69256, 88009, 110331, 136648, 167410, 203091, 244189, 291226, 344748, 405325, 473551, 550044, 635446, 730423, 835665, 951886, 1079824, 1220241, 1373923, 1541680, 1724346

Offset

0,3

Comments

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].

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.

Links

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: x*(1+x)*(1+13*x-2*x^2)/(1-x)^5. - Robert Israel, Nov 07 2016

Example

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.

Maple

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

Prog

(PARI) a(n) = n*(1-3*n+2*n^2+2*n^3)/2 \\ Felix Fröhlich, Nov 07 2016
(PARI) concat(0, Vec(x*(1+x)*(1+13*x-2*x^2)/(1-x)^5 + O(x^40))) \\ Felix Fröhlich, Nov 07 2016

Crossrefs

Cf. A213820.

Sequence in context: A109513 A173368 A041696 * A080187 A362301 A142170

Adjacent sequences: A277974 A277975 A277976 * A277978 A277979 A277980

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 07 2016

Status

approved