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A017113 a(n) = 8*n+4. 34
4, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388, 396, 404, 412, 420, 428, 436, 444, 452, 460, 468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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, Mar 23 2002

Continued fraction expansion of tanh(1/4). - Benoit Cloitre, 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, 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-subsets of X intersecting each Y_i (i=1,2,3). - Milan Janjic, Aug 26 2007

From the Cody Clifton's reference : "There are no 5/8 commutative groups of order 4 mod 8. The maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of the center of the group is equal to one fourth the order of the group [proof given]". - Jonathan Vos Post, May 23 2012

A007814(a(n)) = 2; A037227(a(n)) = 5. - Reinhard Zumkeller, Jun 30 2012

With the substitution n -> n-2 this is 8n-12, as in the paper by Gu and Hao. - Jonathan Vos Post, Sep 23 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1100

Cody Clifton, Commutativity in non-Abelian Groups, May 06 2010.

Meimei Gu and Rongxia Hao, 3-extra connectivity of 3-ary n-cube networks, arXiv:1309.5083 [cs.DM], Sep 19, 2013.

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

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

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

a(n) = 16*n-a(n-1) with n>0, a(0)=4. - Vincenzo Librandi, Nov 19 2010

a(n) = sum((i^k+1)*(i^(4n-k)+1), k=0..4n), where i=sqrt(-1). - Bruno Berselli, Mar 19 2012

G.f.:(1+x)/x^2*(1 - 1/(x*Q(0) + 1)) where Q(k)= 1 - 1/(9^k - 3*x*81^k/(3*x*9^k - 1/(1 + 1/(3*9^k - 27*x*81^k/(9*x*9^k + 1/Q(k+1)  ))))); (continued fraction ). - Sergei N. Gladkovskii, Apr 12 2013

a(n) = 4*A005408(n). - Omar E. Pol, Apr 17 2016

MATHEMATICA

lst={}; Do[AppendTo[lst, 8*n+4], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)

PROG

(MAGMA) [8*n+4: n in [0..50]]; // Vincenzo Librandi, Apr 26 2011

(Haskell)

a017113 = (+ 4) . (* 8)

a017113_list = [4, 12 ..]  -- Reinhard Zumkeller, Jul 13 2013

(PARI) a(n)=8*n+4 \\ Charles R Greathouse IV, Sep 23 2013

CROSSREFS

First differences of A016742 (even squares). Cf. A078370, A078371.

Cf. A081770 (subsequence).

Sequence in context: A190748 A273253 A031065 * A081770 A062876 A238836

Adjacent sequences:  A017110 A017111 A017112 * A017114 A017115 A017116

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 25 15:14 EDT 2017. Contains 284082 sequences.