%I #47 Feb 20 2023 09:21:51

%S 0,26,54,84,116,150,186,224,264,306,350,396,444,494,546,600,656,714,

%T 774,836,900,966,1034,1104,1176,1250,1326,1404,1484,1566,1650,1736,

%U 1824,1914,2006,2100,2196,2294,2394,2496,2600,2706,2814,2924,3036,3150,3266,3384

%N a(n) = n*(n + 25).

%C a(n) is the Zagreb 1 index of the Mycielskian of the cycle graph C[n]. See p. 205 of the D. B. West reference. - _Emeric Deutsch_, Nov 04 2016

%D Douglas B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001.

%H G. C. Greubel, <a href="/A132767/b132767.txt">Table of n, a(n) for n = 0..5000</a>

%H Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689_Extending_the_Golden_Ratio_and_the_Binet-de_Moivre_Formula">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Mycielskian">Mycielskian</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 2*n + a(n-1) + 24 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010

%F a(n) = n^2 + 25*n. - _Omar E. Pol_, Nov 04 2016

%F From _Chai Wah Wu_, Dec 17 2016: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.

%F G.f.: 2*x*(13 - 12*x)/(1-x)^3. (End)

%F From _Amiram Eldar_, Jan 16 2021: (Start)

%F Sum_{n>=1} 1/a(n) = H(25)/25 = A001008(25)/A102928(25) = 34052522467/223092870000, where H(k) is the k-th harmonic number.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/25 - 19081066231/669278610000. (End)

%F E.g.f.: x*(26 + x)*exp(x). - _G. C. Greubel_, Mar 13 2022

%t Table[n (n + 25), {n, 0, 50}] (* _Bruno Berselli_, Aug 22 2018 *)

%t LinearRecurrence[{3,-3,1},{0,26,54},60] (* _Harvey P. Dale_, Feb 20 2023 *)

%o (PARI) a(n)=n*(n+25) \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [n*(n+25) for n in (0..50)] # _G. C. Greubel_, Mar 13 2022

%Y Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Aug 28 2007