A238017 Least triangular number representable as a sum of n consecutive triangular numbers, or -1 if no such triangular number exists.

0, 1, 10, 10, 55, -1, 210, 120, 120, 1485, 2145, -1, 2080, -1, -1, 56616, 1326, 12561, -1, 1540, 1540, 21736, -1, -1, 52650, 16653, 4950, 26796, 10440, 12880, 7750, -1, -1, 7140, 7140, 154290, -1, 11476, -1, 214840, -1, -1, 207690, 23252790, -1, -1, 6895041, -1, 750925

Offset

1,3

Links

Table of n, a(n) for n=1..49.

Example

a(5) = 55 because 55 is the least triangular number representable as a sum of five consecutive triangular numbers: 55 = 3 + 6 + 10 + 15 + 21.
a(7) = 210 because 210 is the least triangular number representable as a sum of seven consecutive triangular numbers: 210 = 10 + 15 + 21 + 28 + 36 + 45 + 55.
10 appears twice because 10 = 1 + 3 + 6 and 10 = 0 + 1 + 3 + 6.

Mathematica

a[1] = 0; a[n_] := Block[{t, x, y, s = Reduce[n*(-1+3*t^2+3*t*n+n^2)/6 == x*(x+1)/2 && x>0 && t >= 0, {t, x}, Integers]}, If[s === False, -1, y = Min[x /. List @ ToRules @ Expand[s /. C[1] -> 1]]; y*(y+1)/2]]; Array[a, 49] (* Giovanni Resta, Mar 02 2014 *)

Crossrefs

Cf. A000217, A129803, A131557, A238018.

Sequence in context: A003875 A341836 A328530 * A111220 A341253 A106789

Adjacent sequences: A238014 A238015 A238016 * A238018 A238019 A238020

Keyword

sign

Author

Alex Ratushnyak, Feb 17 2014

Extensions

a(6) and a(12)-a(49) from Jon E. Schoenfield and Giovanni Resta, Mar 04 2014

Status

approved