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

0,2

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

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.

Sequence in context: A042348 A042350 A255027 * A255020 A184839 A038848

Adjacent sequences: A132764 A132765 A132766 * A132768 A132769 A132770

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved