This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A304607 a(n) = 252*2^n + 140 (n>=1). 4
 644, 1148, 2156, 4172, 8204, 16268, 32396, 64652, 129164, 258188, 516236, 1032332, 2064524, 4128908, 8257676, 16515212, 33030284, 66060428, 132120716, 264241292, 528482444, 1056964748, 2113929356, 4227858572, 8455717004, 16911433868, 33822867596, 67645735052, 135291469964, 270582939788, 541165879436, 1082331758732 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the first Zagreb index of the nanostar dendrimer G[n] from the Ashrafi et al. reference. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph. The M-polynomial of G[n] is M(G[n]; x,y) = 4*x*y^4 + (18*2^n + 21)*x^2*y^2 + (36*2^n - 9)*x^2*y^3 + 3*x^2*y^4 + 9*x^3*y^4. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 A. R. Ashrafi, A. Karbasioun, and M. V. Diudea, Computing Wiener and detour indices of a new type of nanostar dendrimers, MATCH Commun. Math. Comput. Chem. 65, 2011, 193-200. E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102. Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA From Michael De Vlieger, May 15 2018: (Start) G.f.: 28*x*(23 - 28*x)/(1 - 3*x + 2*x^2). a(n) = 3*a(n - 1) - 2*a(n - 2) for n > 2. (End) MAPLE seq(252*2^n+140, n = 1 .. 40); MATHEMATICA CoefficientList[Series[28*(23 - 28*x)/(1 - 3*x + 2*x^2), {x, 0, 31}], x] (* or *) LinearRecurrence[{3, -2}, {644, 1148}, 32] (* or *) Array[252*2^# + 140 &, 32] (* Michael De Vlieger, May 15 2018 *) PROG (PARI) a(n) = 252*2^n + 140; \\ Altug Alkan, May 15 2018 (PARI) Vec(28*x*(23 - 28*x)/(1 - 3*x + 2*x^2) + O(x^40)) \\ Colin Barker, May 23 2018 (GAP) List([1..40], n->252*2^n+140); # Muniru A Asiru, May 16 2018 CROSSREFS Cf. A304605, A304606, A304608. Sequence in context: A089295 A195808 A260838 * A168626 A216023 A100873 Adjacent sequences:  A304604 A304605 A304606 * A304608 A304609 A304610 KEYWORD nonn,easy AUTHOR Emeric Deutsch, May 15 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)