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A195311 Row sums of A195310.

%I A195311 #24 Jun 26 2019 07:22:29
%S A195311 0,1,3,5,7,10,13,17,21,25,29,33,38,43,48,54,60,66,72,78,84,90,97,104,
%T A195311 111,118,126,134,142,150,158,166,174,182,190,199,208,217,226,235,245,
%U A195311 255,265,275,285,295,305,315,325,335,345,356,367,378,389,400
%N A195311 Row sums of A195310.
%e A195311 If written as an irregular triangle in which row n has length A026741(n+1) then the first differences in row n are always n (see below).
%e A195311 Triangle begins:
%e A195311 0,
%e A195311 1,3,5,
%e A195311 7,10,
%e A195311 13,17,21,25,29,
%e A195311 33,38,43,
%e A195311 48,54,60,66,72,78,84,
%e A195311 90,97,104,111,
%e A195311 118,126,134,142,150,158,166,174,182,
%e A195311 190,199,208,217,226,
%e A195311 235,245,255,265,275,285,295,305,315,325,335,
%e A195311 345,356,367,378,389,400
%t A195311 a1318[n_] := If[EvenQ[n], n (3 n/2 + 1)/4, (n + 1) (3 n + 1)/8];
%t A195311 a[n_] := DeleteCases[Table[n - a1318[k], {k, 1, n}], _?Negative] // Total;
%t A195311 Array[a, 56] (* _Jean-François Alcover_, Jun 26 2019 *)
%o A195311 (Sage)
%o A195311 def A195311(n):
%o A195311     return add(max(0,n-k*(3*k-1)/2)+max(0,n-k*(3*k+1)/2) for k in (1..n))
%o A195311 [A195311(n) for n in (1..56)]  # _Peter Luschny_, Oct 12 2012
%Y A195311 Cf. A001318, A026741, A195309, A195310.
%K A195311 nonn
%O A195311 1,3
%A A195311 _Omar E. Pol_, Sep 21 2011