A185243 - OEIS

A185243

Sum of pairs of triangular numbers whose sum and difference are triangular.

36, 276, 1081, 1770, 5886, 5671, 12246, 16653, 60031, 60726, 147153, 293761, 264628, 257403, 574056, 665281, 477753, 1345620, 1512930, 1450956, 2039190, 1695561, 1682695, 3454506, 3560446, 3932610, 2595781, 3589860, 3969153, 4258821, 8427565, 9003646, 12110581

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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..33.

FORMULA

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

EXAMPLE

a(2) = 276, 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, A185253, A185257, A185258.

Sequence in context: A220159 A202958 A187511 * A014136 A245435 A288963

Adjacent sequences: A185240 A185241 A185242 * A185244 A185245 A185246

KEYWORD

nonn

AUTHOR

Martin Renner, Jan 20 2012

STATUS

approved