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A028895 5 times triangular numbers: 5n(n+1)/2. 26
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, 5175, 5405, 5640 (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

Sum of the numbers from 2n to 3n. - Wesley Ivan Hurt, Nov 27 2015

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 entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: 5*x/(1-x)^3.

a(n) = 5*n*(n+1)/2 = 5*A000217(n).

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

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2. - Wesley Ivan Hurt, Nov 27 2015

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, 45}] (* Zerinvary Lajos, Jul 11 2009 *)

PROG

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

(PARI) a(n)=5*n*(n+1)/2 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000217, A005891, A028896, A046092, A085787, A130520, A195013, A195014, A195142.

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

Sequence in context: A268222 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 May 4 01:58 EDT 2016. Contains 272384 sequences.