0,1

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 12 ).

These are the numbers which end in 11 in their binary expansion; also the numbers for which zeta(2*x+1) needs just 2 terms to be evaluated. - Jorge Coveiro (jorgecoveiro(AT)yahoo.com), Dec 16 2004

a(n) = smallest k such that for every r from 0 to 2n-1 there exist j and i, k >= j > i > 2n-1, such that j - i == r ( mod (2n-1)), with (k,(2n-1))=(j,(2n-1))=(i,(2n-1)) = 1. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 24 2003

Apart from initial terms, same as 4n-9.

Campbell reference shows: "A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted." - Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 18 2007

Tanya Khovanova, Recursive Sequences

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))

William A. Stein, The modular forms database

J. Campbell, T.W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues and S. Williams, Intrinsic knotting and linking of almost complete graphs, 15 Jan 2007.

Binary expansion ends 11.

G.f.: (3+x)/(1-x)^2 - Paul Barry (pbarry(AT)wit.ie), Feb 27 2003

Complement of A004773. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 29 2005

seq( (3+4*x), x=0..100 );

a:=n->sum(sum(binomial(2, j), j=0..k), k=1..n): seq(a(n), n=1..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007

a[1]:=-1:for n from 2 to 100 do a[n]:=a[n-1]+4 od: seq(a[n], n=2..49); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008

with(finance):seq(add(cashflows([0, 0, 4], 0 ), k=1..n)-1, n=1..48); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2008

Sequence in context: A059554 A131098 A103543 this_sequence A118894 A039957 A079422

Adjacent sequences: A004764 A004765 A004766 this_sequence A004768 A004769 A004770

nonn,easy

njas