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A028895 5 times triangular numbers: 5n(n+1)/2. 24
0, 5, 15, 30, 50, 75, 105, 140, 180, 225, 275, 330, 390, 455, 525, 600, 680, 765, 855, 950, 1050, 1155, 1265, 1380, 1500, 1625, 1755, 1890, 2030, 2175, 2325, 2480, 2640, 2805, 2975, 3150, 3330, 3515, 3705, 3900, 4100, 4305, 4515, 4730, 4950 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 5, ... and the same line from 0, in the direction 0, 15, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. Axis perpendicular to A195142 in the same spiral. - Omar E. Pol, Sep 18 2011

Bisection of A195014. Sequence found by reading the line from 0, in the direction 0, 5, ..., and the same line from 0, in the direction 0, 15, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is the main diagonal of the spiral. - Omar E. Pol, Sep 25 2011

a(n) = the Wiener index of the graph obtained by applying Mycielski's construction to the complete graph K(n) (n>=2). - Emeric Deutsch, Aug 29 2013

REFERENCES

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

R. Balakrishnan, S. F. Raj, The Wiener number of powers of the Mycielskian, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).

Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 5*n*(n+1)/2 = 5*A000217(n). G.f.: 5*x/(1-x)^3.

a(n) = 5*n+a(n-1). - Vincenzo Librandi, Aug 05 2010

a(n) = A005891(n) - 1. - Omar E. Pol, Oct 03 2011

a(n) = A130520(5n+4). - Philippe Deléham, Mar 26 2013

MAPLE

[seq(5*binomial(n, 2), n=1..45)]; # Zerinvary Lajos, Nov 24 2006

MATHEMATICA

s=0; lst={}; Do[s+=n; AppendTo[lst, s], {n, 0, 7!, 5}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)

Table[Sum[i + 2*n - 1, {i, 2, n}], {n, 1, 45}] (* Zerinvary Lajos, Jul 11 2009 *)

PROG

(MAGMA) [ 5*n*(n+1)/2 : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014

CROSSREFS

Cf. A005891, A046092, A028896.

Cf. A000217. [From Omar E. Pol, Dec 12 2008]

Cf. index to numbers of the form n*(d*n+10-d)/2 in A140090.

Sequence in context: A188350 A078905 A059160 * A194150 A246817 A010898

Adjacent sequences:  A028892 A028893 A028894 * A028896 A028897 A028898

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org), Dec 11 1999

STATUS

approved

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Last modified September 23 12:24 EDT 2014. Contains 247167 sequences.