This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A302981 Number of ways to write n as x^2 + 2*y^2 + 2^z + 2^w, where x,y,z,w are nonnegative integers with z <= w. 13
 0, 1, 2, 3, 4, 5, 4, 5, 5, 6, 7, 8, 7, 8, 6, 6, 7, 9, 8, 11, 12, 9, 7, 10, 8, 11, 11, 11, 10, 9, 6, 8, 10, 11, 14, 16, 12, 12, 11, 12, 13, 17, 13, 13, 13, 10, 7, 11, 12, 13, 15, 15, 14, 14, 8, 15, 14, 13, 15, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Clearly, a(2*n) > 0 if a(n) > 0. We note that 52603423 is the first value of n > 1 with a(n) = 0. See also A302982 and A302983 for related things. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, Refining Lagrange's four-square theorem, J. Number Theory 175(2017), 167-190. Zhi-Wei Sun, New conjectures on representations of integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), no. 2, 97-120. Zhi-Wei Sun, Restricted sums of four squares, arXiv:1701.05868 [math.NT], 2017-2018. EXAMPLE a(2) = 1 with 2 = 0^2 + 2*0^2 + 2^0 + 2^0. a(3) = 2 with 3 = 1^2 + 2*0^2 + 2^0 + 2^0 = 0^2 + 2*0^2 + 2^0 + 2^1. MATHEMATICA SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]; f[n_]:=f[n]=FactorInteger[n]; g[n_]:=g[n]=Sum[Boole[MemberQ[{5, 7}, Mod[Part[Part[f[n], i], 1], 8]]&&Mod[Part[Part[f[n], i], 2], 2]==1], {i, 1, Length[f[n]]}]==0; QQ[n_]:=QQ[n]=(n==0)||(n>0&&g[n]); tab={}; Do[r=0; Do[If[QQ[n-2^k-2^j], Do[If[SQ[n-2^k-2^j-2x^2], r=r+1], {x, 0, Sqrt[(n-2^k-2^j)/2]}]], {k, 0, Log[2, n]-1}, {j, k, Log[2, Max[1, n-2^k]]}]; tab=Append[tab, r], {n, 1, 60}]; Print[tab] CROSSREFS Cf. A000079, A000290, A002479, A271518, A281976, A299924, A299537, A299794, A300219, A300362, A300396, A300441, A301376, A301391, A301471, A301472, A302920, A302982, A302983. Sequence in context: A291520 A317646 A305748 * A205785 A303235 A282062 Adjacent sequences:  A302978 A302979 A302980 * A302982 A302983 A302984 KEYWORD nonn AUTHOR Zhi-Wei Sun, Apr 16 2018 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.

Last modified February 22 06:24 EST 2019. Contains 320389 sequences. (Running on oeis4.)