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 A185243 Sum of pairs of triangular numbers whose sum and difference are triangular. 7

%I

%S 36,276,1081,1770,5886,5671,12246,16653,60031,60726,147153,293761,

%T 264628,257403,574056,665281,477753,1345620,1512930,1450956,2039190,

%U 1695561,1682695,3454506,3560446,3932610,2595781,3589860,3969153,4258821,8427565,9003646,12110581

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

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

%F a(n) = A185128(n) + A185129(n). - _Michel Marcus_, Jan 08 2015

%e 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.

%o (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

%Y Cf. A000217, A185128, A185129, A185223, A185233, A185253, A185257, A185258.

%K nonn

%O 1,1

%A _Martin Renner_, Jan 20 2012

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Last modified June 12 14:32 EDT 2021. Contains 344957 sequences. (Running on oeis4.)