OFFSET
0,2
COMMENTS
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
REFERENCES
Douglas B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Wikipedia, Mycielskian.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 2*n + a(n-1) + 24 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(n) = n^2 + 25*n. - Omar E. Pol, Nov 04 2016
From Chai Wah Wu, Dec 17 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: 2*x*(13 - 12*x)/(1-x)^3. (End)
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(25)/25 = A001008(25)/A102928(25) = 34052522467/223092870000, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/25 - 19081066231/669278610000. (End)
E.g.f.: x*(26 + x)*exp(x). - G. C. Greubel, Mar 13 2022
MATHEMATICA
Table[n (n + 25), {n, 0, 50}] (* Bruno Berselli, Aug 22 2018 *)
LinearRecurrence[{3, -3, 1}, {0, 26, 54}, 60] (* Harvey P. Dale, Feb 20 2023 *)
PROG
(PARI) a(n)=n*(n+25) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+25) for n in (0..50)] # G. C. Greubel, Mar 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved