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A220053 Partial sums in rows of A130517, triangle read by rows.

%I A220053 #15 Sep 23 2021 09:14:03
%S A220053 1,2,3,3,4,6,4,6,7,10,5,8,9,11,15,6,10,12,13,16,21,7,12,15,16,18,22,
%T A220053 28,8,14,18,20,21,24,29,36,9,16,21,24,25,27,31,37,45,10,18,24,28,30,
%U A220053 31,34,39,46,55,11,20,27,32,35,36,38,42,48,56,66,12,22,30
%N A220053 Partial sums in rows of A130517, triangle read by rows.
%H A220053 Reinhard Zumkeller, <a href="/A220053/b220053.txt">Table of n, a(n) for n = 1..7260</a>
%F A220053 T(n,k) = Sum_{i=1..k} A130517(n, i).
%e A220053 1;
%e A220053 2, 3;
%e A220053 3, 4, 6;
%e A220053 4, 6, 7, 10;
%e A220053 5, 8, 9, 11, 15;
%e A220053 6, 10, 12, 13, 16, 21;
%e A220053 7, 12, 15, 16, 18, 22, 28;
%e A220053 8, 14, 18, 20, 21, 24, 29, 36;
%e A220053 9, 16, 21, 24, 25, 27, 31, 37, 45;
%e A220053 10, 18, 24, 28, 30, 31, 34, 39, 46, 55;
%e A220053 11, 20, 27, 32, 35, 36, 38, 42, 48, 56, 66;
%t A220053 T[n_, 1] := n;
%t A220053 T[n_, n_] := n-1;
%t A220053 T[n_, k_] := Abs[2k - n - If[2k <= n+1, 2, 1]];
%t A220053 row[n_] := Table[T[n, k], {k, 1, n}] // Accumulate;
%t A220053 Table[row[n], {n, 1, 12}] // Flatten (* _Jean-François Alcover_, Sep 23 2021 *)
%o A220053 (Haskell)
%o A220053 a220053 n k = a220053_tabl !! (n-1) !! (k-1)
%o A220053 a220053_row n = a220053_tabl !! (n-1)
%o A220053 a220053_tabl = map (scanl1 (+)) a130517_tabl
%o A220053 -- _Reinhard Zumkeller_, Dec 03 2012
%Y A220053 Cf. A000027 (left edge), A000217 (right edge), A000290 (central terms), A002717 (row sums); A220075.
%K A220053 nonn,tabl,easy
%O A220053 1,2
%A A220053 _Reinhard Zumkeller_, Dec 03 2012