0,2

b(n)=a(n-3) is the number of asymmetric nonnegative integer 2 X 2 matrices with sum of elements equal to n, under action of dihedral group D_4(b(0)=b(1)=b(2)=0). G.f. for b(n) is x^3/((1-x)^2*(1-x^2)*(1-x^4)) - Vladeta Jovovic (vladeta(AT)eunet.rs), May 07 2000

If the offset is changed to 5, this is the 2nd Witt transform of A004526 [Moree]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]

T. D. Noe, Table of n, a(n) for n=0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 197

Pieter Moree, The formal series Witt transform, Discr. Math. no. 295 vol. 1-3 (2005) 143-160. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]

For a formula for a(n) see A014557.

a(n)=7/8+n^3/48+n^2/4+85*n/96+A056594(n+3)/8+(-1)^n*(n+4)/32. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]

a(n)=2*sum{k=0..floor(n/2), A0002620(k+2)}-A0002620(n/2+2)(1+(-1)^n)/2. [From Paul Barry (pbarry(AT)wit.ie), Mar 05 2009]

G.f.: 1/((1-x)^4*(1+x)^2*(1+x^2)) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 20 2009]

There are 10 asymmetric nonnegative integer 2 X 2 matrices with sum of elements equal to 7 under action of D_4:

[0 0] [0 0] [0 0] [0 1] [0 1] [0 1] [0 1] [0 2] [0 2] [1 1]

[1 6] [2 5] [3 4] [2 4] [3 3] [4 2] [5 1] [3 2] [4 1] [2 3].

1/((1-x)^2*(1-x^2)*(1-x^4));

(PARI) a(n)=(84+12*(-1)^n+6*I*((-I)^n-I^n)+(85+3*(-1)^n)*n+24*n^2+2*n^3)/96 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 20 2009]

Cf. A014557, A005232, A053307.

Sequence in context: A094589 A071425 A115065 this_sequence A001307 A088932 A088954

Adjacent sequences: A008801 A008802 A008803 this_sequence A008805 A008806 A008807

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).