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A304514
a(n) = 33*2^n - 45 (n>=1).
4
21, 87, 219, 483, 1011, 2067, 4179, 8403, 16851, 33747, 67539, 135123, 270291, 540627, 1081299, 2162643, 4325331, 8650707, 17301459, 34602963, 69205971, 138411987, 276824019, 553648083, 1107296211, 2214592467, 4429184979, 8858370003, 17716740051, 35433480147, 70866960339, 141733920723, 283467841491, 566935683027, 1133871366099
OFFSET
1,1
COMMENTS
a(n) is the number of edges of the nanostar dendrimer D[n] from the Ghorbani et al. reference.
LINKS
M. Ghorbani and M. Songhori, Some topological indices of nanostar dendrimers, Iranian J. Math. Chemistry, 1, No. 2, 2010, 57-65.
FORMULA
From Colin Barker, May 15 2018: (Start)
G.f.: 3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MAPLE
seq(33*2^n-45, n = 1 .. 40);
MATHEMATICA
Rest@ CoefficientList[Series[3 x (7 + 8 x)/((1 - x) (1 - 2 x)), {x, 0, 35}], x] (* or *)
LinearRecurrence[{3, -2}, {21, 87}, 35] (* or *)
Array[33*2^# - 45 &, 35] (* Michael De Vlieger, May 15 2018 *)
PROG
(GAP) List([1..40], n->33*2^n-45); # Muniru A Asiru, May 15 2018
(PARI) a(n) = 33*2^n - 45; \\ Altug Alkan, May 15 2018
(PARI) Vec(3*x*(7 + 8*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 15 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 15 2018
STATUS
approved