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A224436
The hyper-Wiener index of the polyphenylene dendrimer G[n] defined pictorially in the N. E. Arif et al. reference.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 06 2013
STATUS
approved