A025708 -id:A025708 - cp's OEIS frontend

A033438 Number of edges in 6-partite Turán graph of order n.

0, 0, 1, 3, 6, 10, 15, 20, 26, 33, 41, 50, 60, 70, 81, 93, 106, 120, 135, 150, 166, 183, 201, 220, 240, 260, 281, 303, 326, 350, 375, 400, 426, 453, 481, 510, 540, 570, 601, 633, 666, 700, 735, 770, 806, 843, 881

Offset: 0

N. J. A. Sloane

Apart from the initial term this is the elliptic troublemaker sequence R_n(1,6) (also sequence R_n(5,6)) in the notation of Stange (see Table 1, p.16). For other elliptic troublemaker sequences R_n(a,b) see the cross references below. - Peter Bala, Aug 12 2013

Graham et al., Handbook of Combinatorics, Vol. 2, p. 1234.

K. E. Stange, Integral points on elliptic curves and explicit valuations of division polynomials, arXiv:1108.3051 [math.NT], 2011-2014.
Eric Weisstein's World of Mathematics, Turán Graph [_Reinhard Zumkeller_, Nov 30 2009]
Wikipedia, Turán graph [_Reinhard Zumkeller_, Nov 30 2009]
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1).

Differs from A025708(n)+1 at 31st position.
Cf. A002620, A000212, A033436, A033437, A033439, A033440, A033441, A033442, A033443, A033444. [From Reinhard Zumkeller, Nov 30 2009]
Elliptic troublemaker sequences: A007590 (= R_n(2,4)), A030511 (= R_n(2,6) = R_n(4,6)), A184535 (= R_n(2,5) = R_n(3,5)).

a[n_] := Floor[5n^2/12];
Table[a[n], {n, 0, 46}] (* Jean-François Alcover, Jul 31 2018, after Peter Bala *)

a(n) = Sum_{k=0..n} A097325(k)*(n-k). - Reinhard Zumkeller, Nov 30 2009
a(n) = +2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8).
G.f.: -x^2*(1+x+x^3+x^4+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^3 ).
a(n) = floor(5*n^2/12). - Peter Bala, Aug 12 2013
a(n) = Sum_{i=1..n} floor(5*i/6). - Wesley Ivan Hurt, Sep 12 2017

A025723 Index of 7^n within sequence of numbers of form 5^i*7^j.

Original entry on oeis.org

1, 3, 6, 10, 15, 22, 30, 39, 49, 60, 73, 87, 102, 118, 135, 154, 174, 195, 217, 240, 265, 291, 318, 346, 376, 407, 439, 472, 506, 542, 579, 617, 656, 696, 738, 781, 825, 870, 916, 964, 1013, 1063, 1114, 1166, 1220, 1275, 1331, 1388, 1447, 1507, 1568, 1630, 1693

Offset: 0

David W. Wilson

Positions of zeros in A025652. - R. J. Mathar, Jul 06 2025

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A025708, A022330, A022331, etc.

ListTools:-PartialSums([1,seq(ceil(k*log[5](7)),k=1..100)]); # Robert Israel, Nov 16 2016

Table[1 + Sum[Ceiling[k Log[5, 7]], {k, n}], {n, 0, 52}] (* Michael De Vlieger, Nov 16 2016 *)

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=7, 5)); \\ Charles R Greathouse IV, Jan 11 2018

first(n)=my(s, N=1/7); vector(n+1, i, s+=logint(N*=7, 5)+1) \\ Charles R Greathouse IV, Jan 11 2018

a(n) = 1 + Sum_{k=1..n} ceiling(k*log_5(7)). - Robert Israel, Nov 16 2016

Offset changed to 0 by Robert Israel, Nov 16 2016

cp's OEIS Frontend

A033438 Number of edges in 6-partite Turán graph of order n.

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