login
A082660
Number of ways n can be expressed as the sum of a square and a triangular number.
5
1, 1, 1, 1, 1, 1, 2, 0, 0, 3, 1, 1, 0, 1, 2, 1, 1, 0, 3, 0, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 0, 0, 1, 1, 4, 0, 1, 2, 0, 1, 0, 1, 2, 3, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 0, 0, 3, 1, 1, 2, 0, 0, 4, 1, 1, 0, 1, 1, 0, 1, 1, 2, 1, 1, 3, 0, 1, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 1
OFFSET
1,7
COMMENTS
It is assumed here that 0 is a square but not a triangular number. - Amiram Eldar, Dec 08 2019
The greedy inverse (positions of the first occurrence of n) is 1, 7, 10, 37, 136, 235, 1225, 631, 2116, 4789, 11026, 3997, 148240, 19045, 20827, 25876, ... - R. J. Mathar, Apr 28 2020
LINKS
EXAMPLE
a(631) = 8 because:
1. 631 = 6 + 625
2. 631 = 55 + 576
3. 631 = 190 + 441
4. 631 = 231 + 400
5. 631 = 406 + 225
6. 631 = 435 + 196
7. 631 = 595 + 36
8. 631 = 630 + 1
MAPLE
A082660 := proc(n)
local a, tidx, t;
a := 0 ;
for tidx from 1 do
t := A000217(tidx) ;
if t > n then
break;
end if;
if issqr(n-t) then
a := a+1 ;
end if;
end do:
a ;
end proc: # R. J. Mathar, Apr 28 2020
MATHEMATICA
a[n_] := Length @ Solve[x^2 + y (y + 1)/2 == n && x >= 0 && y > 0, {x, y}, Integers]; Array[a, 100] (* Amiram Eldar, Dec 08 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jason Earls, May 17 2003
STATUS
approved