OFFSET
0,2
COMMENTS
Also row sums of A239931, hence the sequence has a symmetric representation. - Omar E. Pol, Aug 30 2015
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10001
M. D. Hirschhorn, The number of representations of a number by various forms, Discrete Mathematics 298 (2005), 205-211.
FORMULA
a(n) = sigma(4n+1) where sigma(n) = A000203(n) is the sum of the divisors of n.
Euler transform of period 4 sequence [ 6, -8, 6, -4, ...]. - Michael Somos, Jul 04 2006
Expansion of q^(-1/4)eta^14(q^2)/(eta^6(q)eta^4(q^4)) in powers of q. - Michael Somos, Jul 04 2006
Expansion of psi(q)^2*phi(q)^2, i.e., convolution of A004018 and A008441 [Hirschhorn]. - R. J. Mathar, Mar 24 2011
Sum_{k=0..n} a(k) = (Pi^2/4) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 17 2022
EXAMPLE
a(1) = 6 since we can write 1 = 1^2 + 0^2 + 0 + 0 = (-1)^2 + 0^2 + 0 + 0 = 0^2 + 1^2 + 0 + 0 = 0^2 + (-1)^2 + 0 + 0 = 0^2 + 0^2 + 1 + 0 = 0^2 + 0^2 + 0 + 1
MATHEMATICA
Table[DivisorSigma[1, 4 n + 1], {n, 0, 57}] (* Michael De Vlieger, Aug 31 2015 *)
PROG
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^14/eta(x+A)^6/eta(x^4+A)^4, n))} /* Michael Somos, Jul 04 2006 */
(Magma) [DivisorSigma(1, 4*n+1): n in [0..60]]; // Vincenzo Librandi, Sep 18 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
James A. Sellers, Dec 21 2005
STATUS
approved