The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A224436 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#12 by Bruno Berselli at Wed May 30 10:28:13 EDT 2018

STATUS

proposed

approved

#11 by Bruno Berselli at Wed May 30 05:37:37 EDT 2018

STATUS

editing

proposed

#10 by Bruno Berselli at Wed May 30 05:37:22 EDT 2018

FORMULA

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

STATUS

proposed

editing

#9 by Colin Barker at Wed May 30 05:32:45 EDT 2018

STATUS

editing

proposed

#8 by Colin Barker at Wed May 30 05:32:11 EDT 2018

LINKS

Colin Barker, <a href="/A224436/b224436.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (19,-150,636,-1560,2208,-1664,512).

FORMULA

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

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

KEYWORD

nonn,changed,easy

STATUS

proposed

editing

#7 by Michel Marcus at Wed May 30 05:00:00 EDT 2018

STATUS

editing

proposed

#6 by Michel Marcus at Wed May 30 04:59:56 EDT 2018

FORMULA

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

#5 by Michel Marcus at Wed May 30 04:59:01 EDT 2018

REFERENCES

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.

LINKS

N. E. Arif, Roslan Hasni and Saeid Alikhani, <a href="http://dx.doi.org/10.3923/jas.2012.2279.2282">Fourth order and fourth sum connectivity indices of polyphenylene dendrimers</a>, J. Applied Science, 12 (21), 2012, 2279-2282.

FORMULA

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

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

CROSSREFS

Cf. A224435.

STATUS

approved

editing

#4 by Joerg Arndt at Sun Apr 07 02:43:55 EDT 2013

STATUS

proposed

approved

#3 by Emeric Deutsch at Sat Apr 06 18:35:16 EDT 2013

STATUS

editing

proposed