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%I #12 Aug 28 2016 00:31:16
%S 0,0,1,4,7,11,17,23,30,39,48,58,70,82,95,110,125,141,159,177,196,217,
%T 238,260,284,308,333,360,387,415,445,475,506,539,572,606,642,678,715,
%U 754,793,833,875,917,960,1005,1050,1096,1144,1192,1241,1292,1343,1395
%N a(n) = C(n,2) + floor(n/3).
%C Exponents in Hankel transform A171451.
%C For n>=2 a(n) is the smallest addend in the sums of n terms where all the natural numbers are used once 1+2=3, 4+5+6=15, 7+8+9+10=34, 11+12+13+14+16=66, 17+18+19+20+21+22=117 23+24+25+26+27+28+29=182, 30+31+32+33+35+36+37+38=272. - _Anton Zakharov_, Aug 28 2016
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F G.f.: (1+2x)/((1-x)^3*(1+x+x^2));
%F a(n)=(3n^2-n-2)/6+sqrt(3)*cos(2*pi*n/3+pi/6)/9+sin(2*pi*n/3+pi/6)/3.
%o (PARI) a(n)=n*(3*n-1)\6 \\ _Charles R Greathouse IV_, Aug 28 2016
%Y Cf. A130481 (first differences)
%K easy,nonn
%O 0,4
%A _Paul Barry_, Dec 09 2009
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