A132767 a(n) = n*(n + 25).

0, 26, 54, 84, 116, 150, 186, 224, 264, 306, 350, 396, 444, 494, 546, 600, 656, 714, 774, 836, 900, 966, 1034, 1104, 1176, 1250, 1326, 1404, 1484, 1566, 1650, 1736, 1824, 1914, 2006, 2100, 2196, 2294, 2394, 2496, 2600, 2706, 2814, 2924, 3036, 3150, 3266, 3384

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• nonn
• easy

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).

Crossrefs

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.

Programs

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 *)

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

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