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A008586 Multiples of 4. 95
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 (list; graph; refs; listen; history; text; internal format)
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 n-set and Y and Z disjoint 2-subsets of X then a(n-3) is equal to the number of 3-subsets 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 n-1 u's. Example: if n=1 then n-1 =zero (0) u, a(1)=4 because we have v, z, x, y. If n=2 then n-1= 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 = Non-negative zeros of the cycloid generated by a circle of radius 2 rolling along the positive x-axis from zero. [Wesley Ivan Hurt, Jul 01 2013]

Apart from the initial term, number of vertices of minimal path on a n-dimensional cubic lattice (n>1) of side length 2, until a self-avoiding walk gets stuck.  A004767 + 1. - Matthew Lehman, Dec 23 2013

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 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

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

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

G.f.: 4*x/(1-x)^2. - David Wilding, Jun 21 2014

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

(Haskell)

a008586 = (* 4)

a008586_list = [0, 4 ..]  -- Reinhard Zumkeller, May 13 2014

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

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Last modified October 31 01:26 EDT 2014. Contains 248845 sequences.