A224436 The hyper-Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference.

3722, 1132836, 20633828, 209655204, 1629644756, 10870551924, 65747845364, 371694578676, 2000609407220, 10374914467572, 52260870309620, 257180428281588, 1241655454635764, 5899945032398580, 27659536839358196, 128183302103185140, 588138999088428788, 2675081423266133748, 12074040181321512692

Offset

0,1

Comments

a(0) has been checked by the direct computation of the Wiener index (using Maple).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

N. E. Arif, Roslan Hasni and Saeid Alikhani, Fourth order and fourth sum connectivity indices of polyphenylene dendrimers, J. Applied Science, 12 (21), 2012, 2279-2282.

Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).

Formula

a(n) = 407284 + (-2453054 + 211431*n - 103545*n^2)*2^n + (2049492 - 1303920*n + 608400*n^2)*4^n.

G.f.: 2*(1861 + 531059*x - 165878*x^2 - 7414660*x^3 + 13296352*x^4 - 4263232*x^5 + 3512832*x^6)/((1 - x)(1 - 2*x)^3*(1 - 4*x)^3).

a(n) = 19*a(n-1) - 150*a(n-2) + 636*a(n-3) - 1560*a(n-4) + 2208*a(n-5) - 1664*a(n-6) + 512*a(n-7) for n>6. - Colin Barker, May 30 2018

Maple

a := proc (n) options operator, arrow: 407284-2453054*2^n-1303920*4^n*n+211431*2^n*n+608400*4^n*n^2-103545*2^n*n^2+2049492*4^n end proc: seq(a(n), n = 0 .. 18);

Prog

(PARI) Vec(2*(1861 + 531059*x - 165878*x^2 - 7414660*x^3 + 13296352*x^4 - 4263232*x^5 + 3512832*x^6) / ((1 - x)*(1 - 2*x)^3*(1 - 4*x)^3) + O(x^20)) \\ Colin Barker, May 30 2018

Crossrefs

Cf. A224435.

Sequence in context: A289512 A260860 A221013 * A031559 A031739 A251206

Adjacent sequences: A224433 A224434 A224435 * A224437 A224438 A224439

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 06 2013

Status

approved