

A008586


Multiples of 4.


80



0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228
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OFFSET

0,2


COMMENTS

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 14 ).
A000466(n), A008586(n) and A053755(n) are Pythagorean triples.  Zak Seidov, Jan 16 2007
If X is an nset and Y and Z disjoint 2subsets of X then a(n3) is equal to the number of 3subsets of X intersecting both Y and Z.  Milan Janjic, Aug 26 2007
Number of n permutations (n>=1) of 5 objects u, v, z, x, y with repetition allowed, containing n1 u's. Example: if n=1 then n1 =zero (0) u, a(1)=4 because we have v, z, x, y. If n=2 then n1= one (1) u, a(2)=8 because we have vu, zu, xu, yu, uv, uz, ux, uy. A038231 formatted as a triangular array: diagonal :4,8,12,16,20,24,28,32... [Zerinvary Lajos, Aug 06 2008]
For n > 0: numbers having more even than odd divisors: A048272(a(n)) < 0. [Reinhard Zumkeller, Jan 21 2012]
A214546(a(n)) < 0 for n > 0.  Reinhard Zumkeller, Jul 20 2012
A090418(a(n)) = 0 for n > 0.  Reinhard Zumkeller, Aug 06 2012
Terms are the differences of consecutive centered square numbers (A001844).  Mihir Mathur, Apr 02 2013
a(n)*Pi = Nonnegative zeros of the cycloid generated by a circle of radius 2 rolling along the positive xaxis from zero. [Wesley Ivan Hurt, Jul 01 2013]
Apart from the initial term, number of vertices of minimal path on a ndimensional cubic lattice (n>1) of side length 2, until a selfavoiding walk gets stuck. A004767 + 1.  Matthew Lehman, Dec 23 2013


REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, SpringerVerlag, 1976, page 3.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
Milan Janjic, Two Enumerative Functions
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 316
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Eric Weisstein's World of Mathematics, Doubly Even Number
Index to sequences with linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = A008574(n), n>0. [R. J. Mathar, Oct 28 2008]
a(n) = Sum_k>=0 {A030308(n,k)*2^(k+2)}.  Philippe Deléham, Oct 17 2011
a(n+1) = A000290(n+2)  A000290(n).  Philippe Deléham, Mar 31 2013


MAPLE

A008586:=n>4*n; seq(A008586(n), n=0..100); # Wesley Ivan Hurt, Feb 24 2014


MATHEMATICA

Range[0, 500, 4] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)


PROG

(PARI) a(n)=n<<2 \\ Charles R Greathouse IV, Oct 17 2011


CROSSREFS

Cf. A038231, A035008, A004767.
Sequence in context: A076310 A161352 * A059558 A008574 A189917 A172326
Adjacent sequences: A008583 A008584 A008585 * A008587 A008588 A008589


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



