A309783 Numbers that are sums of one or more consecutive positive triangular numbers in more than one way.

10, 36, 55, 64, 100, 120, 136, 164, 210, 276, 361, 435, 460, 514, 560, 596, 676, 760, 1176, 1225, 1320, 1326, 1460, 1484, 1485, 1505, 1540, 1684, 1736, 1770, 1891, 1936, 2014, 2080, 2145, 2180, 2314, 2485, 2596, 2890, 3156, 3244, 3275, 3364, 3486, 3570, 3710, 3916

Offset: 1

Author

Ilya Gutkovskiy, Aug 17 2019

Keywords

• nonn

Comments

The first number that is the sum in three ways is 2180. The first that is the sum in four ways is 10053736. - Robert Israel, Aug 20 2019

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (first 2759 terms from Robert Israel)

Crossrefs

Cf. A000217, A034706, A130052, A307666.

Programs

Maple

N:= 10000: # for terms <= N
V:= Vector(N):
for i from 1 while i*(i+1)/2 <= N do
  s:= i*(i+1)*(i+2)/6;
  for j from i-1 to 0 by -1 do
    t:= j*(j+1)*(j+2)/6;
    if s-t > N then break fi;
    V[s-t]:= V[s-t]+1
  od;
od:
select(t -> V[t]>1, [$1..N]); # Robert Israel, Aug 20 2019

Formula

A307666(a(n)) > 1.