OFFSET
0,6
COMMENTS
Inspired by A278329.
a(n) >= a(n-1), first differences are nondecreasing.
LINKS
Alois P. Heinz and Robert G. Wilson v, Table of n, a(n) for n = 0..20000
EXAMPLE
a(1) .. a(3) = 0;
a(4) = 1 since 2+3+4 = 9;
a(5) = 2 since 2+3+4 = 1+3+5 = 9;
a(6) = 3 since 2+3+4 = 1+3+5 = 1+2+6 = 9;
a(7) = 5 since a(6) = 3 plus 3+6+7 = 4+5+7 = 16;
a(8) = 8 since a(7) = 5 plus 1+7+8 = 2+6+8 = 3+5+8 = 16; etc.
MAPLE
g:= (n, t)-> max(0, iquo(n-1, 2)-max(1, n-t)+1):
b:= n-> add(g(k^2-n, n-1), k=ceil(sqrt(n+3))..floor(sqrt(3*n-3))):
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n)) end:
seq(a(n), n=0..100);
MATHEMATICA
f[n_] := Length@ Select[Plus @@@ Subsets[ Range@ n, {3}], Mod[ Sqrt[#], 1] == 0 &]; Array[f, 65] (* or *)
f = Compile[{{n, _Integer}}, Block[{a = 1, b = 2, c = 3, cnt = 0}, While[a < b, b = a +1; While[b < c, c = b +1; While[c < n +1, If[ Mod[ Sqrt[a + b + c], 1] == 0, cnt++]; c++]; b++]; a++]; cnt]]; Array[f, 65] (* or *)
g = Compile[{{n, _Integer}}, If[n < 4, 0, Block[{a = 1, b = 2, cnt = f[n -1]}, While[a < b, b = a +1; While[b < n, If[ Mod[ Sqrt[a + b + n], 1] == 0, cnt++]; b++]; a++]; cnt]]]; f[n_] := f[n] = g[n]; Array[f, 100]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz and Robert G. Wilson v, Jan 28 2017
STATUS
approved