A185253 Difference of pairs of triangular numbers whose sum and difference are triangular.

6, 66, 325, 210, 1596, 2701, 1326, 903, 1225, 16836, 6903, 82621, 141778, 181503, 63546, 52975, 354903, 10440, 13530, 405450, 7140, 989121, 1329265, 511566, 668746, 437580, 2102275, 2001000, 2469753, 3229611, 1428895, 3096316, 1963171, 6843150, 856086, 4276350

Offset

1,1

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8.

Links

Table of n, a(n) for n=1..36.

Formula

a(n) = A185128(n) - A185129(n). - Michel Marcus, Jan 08 2015

Example

a(2) = 66, since the pair of triangular numbers 171 = 18*(18+1)/2 and 105 = 14*(14+1)/2 produce the sum 276 = 23*(23+1)/2 and the difference 66 = 11*(11+1)/2 which are both triangular numbers.

Prog

(PARI) lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(v[n]-v[k], ", ")); ); ); } \\ Michel Marcus, Jan 08 2015

Crossrefs

Cf. A000217, A185128, A185129, A185223, A185233, A185243, A185257, A185258.

Sequence in context: A119172 A064167 A175455 * A192089 A119073 A028559

Adjacent sequences: A185250 A185251 A185252 * A185254 A185255 A185256

Keyword

nonn

Author

Martin Renner, Jan 20 2012

Status

approved