

A238017


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


1



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
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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



