0,1

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 65 ).

n such that 16 is the largest power of 2 dividing A003629(k)^n-1 for any k. - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 23 2002

Continued fraction expansion of tanh(1/4). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 17 2002

Consider all primitive Pythagorean triples (a,b,c) with c-a=8, sequence gives values for b. (Corresponding values for a are A078371(n), while c follows A078370(n).) - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Nov 19 2004

Also numbers of the form a^2 + b^2 + c^2 + d^2, where a,b,c,d are odd integers. - Alexander Adamchuk (alex(AT)kolmogorov.com), Dec 01 2006

If X is an n-set and Y_i (i=1,2,3) mutually disjoint 2-subsets of X then a(n-5) is equal to the number of 4-subests of X intersecting each Y_i (i=1,2,3). - Milan R. Janjic (agnus(AT)blic.net), Aug 26 2007

Also, except for the first term, a(n)=16*n-a(n-1), (with a(1)=12) Example: for n=2, a(2)=16*2-12=20; n=3, a(3)=16*3-20=28; n=4, a(4)=16*4-28=36 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 22 2009]

Milan Janjic, Two Enumerative Functions

Tanya Khovanova, Recursive Sequences

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))

William A. Stein, The modular forms database

a(n) = A118413(n+1,3) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 27 2006

lst={}; Do[AppendTo[lst, 8*n+4], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 26 2009]

(Other) sage: [i+4 for i in range(355) if gcd(i, 8) == 8] # [From Zerinvary Lajosz (zerinvarylajos(AT)yahoo.com), May 20 2009]

Cf. A078370, A078371.

Sequence in context: A043437 A141065 A031065 this_sequence A081770 A062876 A085039

Adjacent sequences: A017110 A017111 A017112 this_sequence A017114 A017115 A017116

nonn,easy

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