login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A236924 Number of integer solutions to a^2 + 2*b^2 + 2*c^2 + 4*d^2 = n. 16
1, 2, 4, 8, 8, 12, 16, 16, 24, 26, 24, 24, 32, 28, 32, 48, 24, 36, 52, 40, 48, 64, 48, 48, 96, 62, 56, 80, 64, 60, 96, 64, 24, 96, 72, 96, 104, 76, 80, 112, 144, 84, 128, 88, 96, 156, 96, 96, 96, 114, 124, 144, 112, 108, 160, 144, 192, 160, 120, 120, 192, 124, 128, 208, 24, 168, 192, 136, 144, 192, 192 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Olivia X. M. Yao, Ernest X. W. Xia, Combinatorial proofs of five formulas of Liouville, Discrete Math. 318 (2014), 1--9. MR3141622.

FORMULA

Yao and Xia give an explicit formula for a(n) due to Liouville.

G.f.: theta_3(q)*theta_3(q^2)^2*theta_3(q^4), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 03 2018

MAPLE

with(LinearAlgebra);

L:=proc(a, b, c, d, M) local n, hit, ul, vl, wl, xl, u, v, w, x, su, sv, sw, sx;

hit:=Array(0..M); ul:=floor(sqrt(M/a)); vl:=floor(sqrt(M/b));

wl:=floor(sqrt(M/c)); xl:=floor(sqrt(M/d));

for u from -ul to ul do

su:=a*u^2;

for v from -vl to vl do

sv:=su+b*v^2;

for w from -wl to wl do

sw:=sv+c*w^2;

for x from -xl to xl do

sx:=sw+d*x^2;

if sx <= M then hit[sx]:=hit[sx]+1; fi;

od; od; od; od;

[seq(hit[n], n=0..M)];

end;

L(1, 2, 2, 4, 60);

CROSSREFS

Cf. A000118, A320149, A320150, A320151, A320152, A320153.

Sequence in context: A198346 A078750 A054785 * A266575 A260514 A123263

Adjacent sequences:  A236921 A236922 A236923 * A236925 A236926 A236927

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 14 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 17 12:10 EST 2019. Contains 320219 sequences. (Running on oeis4.)