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 (jvospost3(AT)gmail.com), Jan 18 2007

Any (4n+3)-dimensional manifold endowed with a mixed 3-Sasakian structure is an Einstein space with Einstein constant lambda = 4n+2 [Theorem 3, p.10 of Ianus et al]. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 24 2008]

For all n, a(n) is not a^2+b^2. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 27 2009]

If X=(n^3+9)/4, Y=(n^3+9)/2, Z=(n^4+9*n)/4, then X^3+Y^3+Z^3=(X*Y)^2 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jun 30 2009]

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.

Stere Ianus, Mihai Visinescu and Gabriel-Eduard Vilcu, Hidden symmetries and Killing tensors on curved spaces, Nov 21, 2008. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 24 2008]

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)gmail.com), Aug 29 2005

a(n)=2*a(n-1)-a(n-2); a(0)=3, a(1)=7. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]

a(n)=8*n-a(n-1)-6 (with a(1)=3) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]

For n=3, X=9, Y=18, Z=27, and 9^3+18^3+27^3=(9*18)^2; n=7, X=88, Y=176, Z=616, and 88^3+176^3+616^3=(88*176)^2; [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jun 30 2009]

For n=2, a(2)=8*2-3-6=7; n=3, a(3)=8*3-7-6=11; n=4, a(4)=8*4-11-6=15 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 24 2009]

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

f[n_]:=4*n+3; lst={}; Do[a=f[n]; AppendTo[lst, a], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]

(Other) sage: [i+3 for i in range(190) if gcd(i, 4) == 4] # [From Zerinvary Lajosz (zerinvarylajos(AT)yahoo.com), May 20 2009]

(Other) sage: [crt(3, n, 4, 3 ) for n in xrange(3, 51)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]

Sequence in context: A124981 A059554 A103543 this_sequence A131098 A118894 A039957

Adjacent sequences: A004764 A004765 A004766 this_sequence A004768 A004769 A004770

nonn,easy,new

N. J. A. Sloane (njas(AT)research.att.com).