|
| |
|
|
A008586
|
|
Multiples of 4.
|
|
73
|
|
|
|
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 (zerinvarylajos(AT)yahoo.com), 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
|
|
|
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
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
|
|
|
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.
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
|
| |
|
|
