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A216123
The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Ashrafi et al. reference.
1
657339, 15126495, 170253735, 1399219767, 9656453079, 59728974615, 342996234135, 1867389894807, 9768453728919, 49540857757335, 245123724445335, 1188721211741847, 5669374461982359, 26661906782549655, 123891350653597335, 569765357115700887, 2596763217388533399
OFFSET
1,1
COMMENTS
a(1) has been checked by the direct computation of the hyper-Wiener index (using Maple).
LINKS
A. R. Ashrafi and M. Mirzagar, PI, Szeged and edge Szeged indices of an infinite family of nanostar dendrimers, Indian J. of Chemistry, 47A, 2008, 538-541.
M. Rostami, M. Shabanian, and H. Moghanian, Some topological indices for theoretical study of two types of nanostar dendrimers, Digest J. of Nanomaterials and Biostructures, 7, No. 1, 2012, 247-252.
J. Yang, F. Xia, and S. Chen, Second-order and third-order connectivity indices of an infinite family of dendrimer nanostars, Int. J. Contemp. Math. Sciences, 6, 2011, No. 5, 215-220.
Index entries for linear recurrences with constant coefficients, signature (19,-150,636,-1560,2208,-1664,512).
FORMULA
a(n) = -685719 - 2949654*2^n + 2264412*4^n + 495780*n*2^n - 1584720*n*4^n - 136500*n^2*2^n + 608400*n^2*4^n.
G.f.: -3*x*(81408*x^6 +1294464*x^5 +4778592*x^4 +5101816*x^3 -6182940*x^2 +879018*x +219113) / ((x -1)*(2*x -1)^3*(4*x -1)^3). - Colin Barker, Apr 01 2013
MAPLE
a := proc (n) options operator, arrow: 685719-2949654*2^n+2264412*4^n-1584720*4^n*n+495780*2^n*n-136500*2^n*n^2+608400*4^n*n^2 end proc: seq(a(n), n = 1 .. 17);
CROSSREFS
Cf. A216122.
Sequence in context: A365024 A287591 A308086 * A282356 A114678 A254495
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Mar 25 2013
STATUS
approved