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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
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OFFSET
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0,1
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COMMENTS
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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
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 in Clifton reference). [Jonathan Vos Post, May 23 2012]
A007814(a(n)) = 2; A037227(a(n)) = 5. - Reinhard Zumkeller, Jun 30 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1100
Cody Clifton, Commutativity in non-Abelian Groups, May 6 2010.
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 to sequences with linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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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
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MATHEMATICA
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lst={}; Do[AppendTo[lst, 8*n+4], {n, 0, 6!}]; lst [From Vladimir Joseph Stephan Orlovsky, Feb 26 2009]
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PROG
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(MAGMA) [8*n+4: n in [0..50]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
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First differences of A016742 (even squares). Cf. A078370, A078371.
Sequence in context: A141065 A190748 A031065 * A081770 A062876 A085039
Adjacent sequences: A017110 A017111 A017112 * A017114 A017115 A017116
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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