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Sums of rows of the triangle in A139325.
2

%I #8 Sep 27 2024 05:37:40

%S 0,3,6,10,14,19,24,30,36,45,52,60,67,76,86,96,105,117,127,138,151,162,

%T 176,189,203,216,230,246,262,277,292,308,325,343,362,376,398,417,435,

%U 451,473,491,515,535,557,579,599,622,646,668,691,712,737,764,788,815

%N Sums of rows of the triangle in A139325.

%C a(n) = Sum_{k=1..n} A139325(n,k).

%F a(n) = A000720(2*n^2 - 1) - 1.

%e a(4) = #{3,5,7}+#{11,13}+#{17,19,23}+#{29,31} = 3+2+3+2 = 10:

%e ..1 ...3 ...5 ...7 ... primes in first row = {3,5,7},

%e ..9 ..11 ..13 ..15 ... primes in 2nd row = {11,13},

%e .17 ..19 ..21 ..23 ... primes in 3rd row = {17,19,23},

%e .25 ..27 ..29 ..31 ... primes in 4th row = {29,31}.

%Y Cf. A000720, A038107, A139325.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Apr 14 2008