A193396 -id:A193396 - cp's OEIS frontend

A193397 Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).

109, 271, 553, 955, 1541, 2279, 3265, 4435, 5917, 7615, 9689, 12011, 14773, 17815, 21361, 25219, 29645, 34415, 39817, 45595, 52069, 58951, 66593, 74675, 83581, 92959, 103225, 113995, 125717, 137975, 151249, 165091, 180013, 195535, 212201, 229499, 248005, 267175, 287617

Offset: 2

Emeric Deutsch, Jul 25 2011

Vincenzo Librandi, Table of n, a(n) for n = 2..10000
A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems , Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396.

[4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011

a := proc (n) options operator, arrow: 4*n^3+20*n^2-12*n+2*(-1)^n*(n-2)+21 end proc: seq(a(n), n = 2 .. 40);

Table[4n^3+20n^2-12n+2(-1)^n(n-2)+21,{n,2,40}] (* or *) LinearRecurrence[ {2,1,-4,1,2,-1},{109,271,553,955,1541,2279},39] (* Harvey P. Dale, Aug 26 2011 *)

a(n) = 4*n^3 + 20*n^2 - 12*n + 2*(-1)^n*(n-2) + 21.
G.f.: x^2*(109+53*x-98*x^2+14*x^3+53*x^4-35*x^5)/((1+x)^2*(1-x)^4). - Bruno Berselli, Jul 27 2011
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6), with a(2)=109, a(3)=271, a(4)=553, a(5)=955, a(6)=1541, a(7)=2279. - Harvey P. Dale, Aug 26 2011

A193398 Hyper-Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n >= 2, s = 21; see the Gutman et al. reference).

Original entry on oeis.org

215, 636, 1557, 3018, 5555, 8968, 14225, 20790, 30159, 41364, 56525, 74146, 97067, 123168, 156105, 193038, 238535, 288940, 349829, 416634, 496035, 582456, 683777, 793318, 920255, 1056708, 1213245, 1380690, 1571099, 1773904, 2002745, 2245566, 2517687, 2805468

Offset: 2

Emeric Deutsch, Jul 25 2011

Vincenzo Librandi, Table of n, a(n) for n = 2..10000
A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397.

[(3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: n in [2..40]]; // Vincenzo Librandi, Jul 26 2011

a := n -> (3/2)*n^4+12*n^3+(3/2)*n^2*(-1)^n+(73/2)*n^2+6*n*(-1)^n-79*n+(83/4)*(-1)^(n+1)+439/4: seq(a(n), n = 2 .. 35);

LinearRecurrence[{2,2,-6,0,6,-2,-2,1},{215,636,1557,3018,5555,8968,14225,20790},40] (* Harvey P. Dale, Aug 30 2017 *)

a(n)=(6*n^4+48*n^3+146*n^2-316*n+439+(-1)^n*(6*n^2+24*n-83))/4 \\ Charles R Greathouse IV, Jul 28 2011

a(n) = (6*n^4 + 48*n^3 + 146*n^2 - 316*n + 439 + (-1)^n*(6*n^2 + 24*n - 83))/4.

G.f.: x^2*(215 + 206*x - 145*x^2 - 78*x^3 + 221*x^4 - 126*x^5 - 99*x^6 + 94*x^7)/((1+x)^3*(1-x)^5). - Bruno Berselli, Jul 26 2011

A193399 Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

Original entry on oeis.org

27, 109, 271, 545, 931, 1493, 2199, 3145, 4267, 5693, 7327, 9329, 11571, 14245, 17191, 20633, 24379, 28685, 33327, 38593, 44227, 50549, 57271, 64745, 72651, 81373, 90559, 100625, 111187, 122693, 134727

Offset: 1

Emeric Deutsch, Jul 25 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397, A193398.

[4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

a := proc (n) options operator, arrow: 4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 end proc: seq(a(n), n = 1 .. 40);

a(n)=4*n^3+16*n^2+8*n+2*(-1)^n*(n-2)-3 \\ Charles R Greathouse IV, Jul 28 2011

a(n) = 4*n^3 + 16*n^2 + 8*n + 2*(-1)^n*(n - 2) - 3.

G.f.: x*(27 + 55*x + 26*x^2 + 2*x^3 - 21*x^4 + 7*x^5)/((1+x)^2*(1-x)^4). - Bruno Berselli, Jul 27 2011

A193400 Hyper-Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

Original entry on oeis.org

42, 215, 636, 1513, 2862, 5211, 8352, 13229, 19314, 28063, 38532, 52785, 69366, 91043, 115752, 147061, 182202, 225639, 273804, 332153, 396222, 472555, 555696, 653373, 759042, 881711, 1013652, 1165249, 1327494, 1512243, 1709112, 1931525, 2167626, 2432503, 2712732

Offset: 1

Emeric Deutsch, Jul 25 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
A. A. Dobrynin, I. Gutman, S. Klavzar, P. Zigert, Wiener Index of Hexagonal Systems, Acta Applicandae Mathematicae 72 (2002), pp. 247-294.
I. Gutman, S. Klavzar, M. Petkovsek, and P. Zigert, On Hosoya polynomials of benzenoid graphs, Comm. Math. Comp. Chem. (MATCH), 43, 2001, 49-66.
Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Cf. A143937, A143938, A193391, A193392, A193393, A193394, A193395, A193396, A193397, A193398, A193399.

[(6*n^4 + 40*n^3 + 114*n^2 + 16*n - 45 + (-1)^n*(6*n^2 +20*n -63))/4: n in [1..40]]; // Vincenzo Librandi, Jul 26 2011

a := proc (n) options operator, arrow: (3/2)*n^4+10*n^3+(57/2)*n^2+4*n-45/4+(1/4)*(-1)^n*(6*n^2+20*n-63) end proc: seq(a(n), n = 1 .. 35);

a(n)=(6*n^4+40*n^3+114*n^2+16*n-45+(-1)^n*(6*n^2+20*n-63))/4 \\ Charles R Greathouse IV, Jul 28 2011

a(n) = ( 6*n^4 +40*n^3 +114*n^2 +16*n -45 +(-1)^n*(6*n^2 +20*n -63) )/4.

G.f.: x*(42+131*x+122*x^2+63*x^3-146*x^4+25*x^5+78*x^6-27*x^7)/((1+x)^3*(1-x)^5). - Bruno Berselli, Jul 27 2011

cp's OEIS Frontend

A193397 Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).

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A193398 Hyper-Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n >= 2, s = 21; see the Gutman et al. reference).

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A193399 Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

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Keywords

Links

Crossrefs

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Magma

Maple

PARI

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A193400 Hyper-Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

PARI

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