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A089988 Possible differences of n^2*(n+1)/2. 0

%I #3 Mar 31 2012 13:21:56

%S 5,12,17,22,34,35,39,51,57,69,70,74,86,92,108,117,120,121,125,145,156,

%T 162,176,178,190,195,209,210,213,247,248,262,270,279,282,287,321,330,

%U 354,365,376,386,387,399,404,424

%N Possible differences of n^2*(n+1)/2.

%C Vaguely related to x^3+y^3=z^3, as x^3=2x.A000217(x) - x^2, e.g. 3^3=2.3.6 - 9 = 27.

%F n^2*(n+1)/2 - m^2*(m+1)/2 for all n>m

%e 5^2*(5+1)/2=25*3=75 and 3^2*(3+1)/2=9*2=18, so 75-18=57 is in the sequence

%o (PARI) { v=vector(300); c=0; for (i=1,20, for (j=i,20, v[c++ ]=tn(j)-tn(i))); v=vecsort(v); v }

%Y Cf. A000217, A002411 (pentagonal pyramidal numbers).

%K nonn

%O 1,1

%A _Jon Perry_, Jan 14 2004

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