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

1,1

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)

Formula

A307666(a(n)) > 1.

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

Crossrefs

Cf. A000217, A034706, A130052, A307666.

Sequence in context: A346386 A117404 A359959 * A072517 A271912 A288947

Adjacent sequences: A309780 A309781 A309782 * A309784 A309785 A309786

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 17 2019

Status

approved