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%I #8 Jan 01 2024 02:10:19
%S 1,2,5,6,9,15,16,19,25,35,36,39,45,55,70,71,74,80,90,105,126,127,130,
%T 136,146,161,182,210,211,214,220,230,245,266,294,330,331,334,340,350,
%U 365,386,414,450,495,496,499,505,515,530,551,579,615,660,715,716,719
%N Tetrahedron-tree numbers: a(n)=sum(b(m),m=1..n), b(m)=1, 1,3, 1,3,6, 1,3,6,10,..., 1,2,...,i*(i+1)2.
%H Harvey P. Dale, <a href="/A051677/b051677.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n*(n+1)/2+m) = n*(n+1)*(n+2)*(n+3)/24 + m*(m+1)*(m+2)/6 = A000332(n)+A000292(m), m=0...n+1, n=1, 2, 3, ..
%t With[{nn=20},Accumulate[Flatten[Table[Take[Accumulate[Range[nn]],n],{n,nn}]]]] (* _Harvey P. Dale_, Jan 29 2012 *)
%Y Cf. A000332, A000292.
%K easy,nice,nonn
%O 1,2
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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