A304836 -id:A304836 - cp's OEIS frontend

A304837 a(n) = 6(n - 1)(81*n - 104) for n >= 1.

0, 348, 1668, 3960, 7224, 11460, 16668, 22848, 30000, 38124, 47220, 57288, 68328, 80340, 93324, 107280, 122208, 138108, 154980, 172824, 191640, 211428, 232188, 253920, 276624, 300300, 324948, 350568, 377160, 404724, 433260, 462768, 493248, 524700, 557124, 590520, 624888, 660228, 696540, 733824, 772080, 811308

Offset: 1

Emeric Deutsch, May 21 2018

a(n) is the first Zagreb index of the hex derived network HDN1(n) from the Manuel et al. reference (see HDN1(4) in Fig. 8).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of HDN1(n) is M(HDN1(n); x, y) = 12*x^3*y^5 + (18*(n-2))*x^3*y^7 + (6*(3*n^2-9*n+7))*x^3*y^12 + 12*x^5*y^7 + 6*x^5*y^12 + (6*(n-3))*x^7*y^7 + (12*(n-2))*x^7*y^12 + (3*(n-2)*(3*n-5)*x^12*y^12.
54*a(n) + 529 is a square. - Bruno Berselli, May 22 2018

Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
P. Manuel, R. Bharati, I. Rajasingh, and Chris Monica M, On minimum metric dimension of honeycomb networks, J. Discrete Algorithms, 6, 2008, 20-27.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A082040, A304836, A304838.

List([1..50], n->486*n^2-1110*n+624); # Muniru A Asiru, May 22 2018

Maple
```
seq(624-1110*n+486*n^2, n = 1 .. 45);
```

Table[6 (n - 1) (81 n - 104), {n, 1, 50}] (* Bruno Berselli, May 22 2018 *)

concat(0, Vec(12*x^2*(29 + 52*x)/(1 - x)^3 + O(x^40))) \\ Colin Barker, May 23 2018

G.f.: 12*x^2*(29 + 52*x)/(1 - x)^3. - Bruno Berselli, May 22 2018

A304838 a(n) = 1944n^2 - 5016n + 3138 (n >= 1).

Original entry on oeis.org

66, 882, 5586, 14178, 26658, 43026, 63282, 87426, 115458, 147378, 183186, 222882, 266466, 313938, 365298, 420546, 479682, 542706, 609618, 680418, 755106, 833682, 916146, 1002498, 1092738, 1186866, 1284882, 1386786, 1492578, 1602258, 1715826, 1833282, 1954626, 2079858

Offset: 1

Emeric Deutsch, May 21 2018

a(n) is the second Zagreb index of the hex derived network HDN1(n) from the Manuel et al. reference (see HDN1(4) in Fig. 8).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The M-polynomial of HDN1(n) is M(HDN1(n);x,y) = 12*x^3*y^5 + (18*(n-2))*x^3*y^7 + (6*(3*n^2-9*n+7))*x^3*y^12 + 12*x^5*y^7 + 6*x^5*y^12 + (6*(n-3))*x^7*y^7 + (12*(n-2))*x^7*y^12 + (3*(n-2)*(3*n-5)*x^12*y^12.

Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
P. Manuel, R. Bharati, I. Rajasingh, and Chris Monica M, On minimum metric dimension of honeycomb networks, J. Discrete Algorithms, 6, 2008, 20-27.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A082040, A304836, A304837.

List([1..50], n->1944*n^2-5016*n+3138); # Muniru A Asiru, May 22 2018

seq(3138 - 5016*n + 1944*n^2, n = 1 .. 45);

Table[1944 n^2 - 5016 n + 3138, {n, 1, 40}] (* Bruno Berselli, May 22 2018 *)
LinearRecurrence[{3,-3,1},{66,882,5586},40] (* Harvey P. Dale, Dec 02 2018 *)

Vec(6*x*(11 + 114*x + 523*x^2)/(1 - x)^3 + O(x^40)) \\ Colin Barker, May 23 2018

G.f.: 6*x*(11 + 114*x + 523*x^2)/(1 - x)^3. - Bruno Berselli, May 22 2018

cp's OEIS Frontend

A304837 a(n) = 6(n - 1)(81*n - 104) for n >= 1.

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A304838 a(n) = 1944n^2 - 5016n + 3138 (n >= 1).

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cp's OEIS Frontend

A304837 a(n) = 6*(n - 1)*(81*n - 104) for n >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

Formula

A304838 a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

Formula

A304837 a(n) = 6(n - 1)(81*n - 104) for n >= 1.

A304838 a(n) = 1944n^2 - 5016n + 3138 (n >= 1).