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

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, 28, 8, 14, 18, 20, 21, 24, 29, 36, 9, 16, 21, 24, 25, 27, 31, 37, 45, 10, 18, 24, 28, 30, 31, 34, 39, 46, 55, 11, 20, 27, 32, 35, 36, 38, 42, 48, 56, 66, 12, 22, 30

Offset: 1

Author

Reinhard Zumkeller, Dec 03 2012

Keywords

• nonn
• tabl
• easy

Examples

			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, 28;
8, 14, 18, 20, 21, 24, 29, 36;
9, 16, 21, 24, 25, 27, 31, 37, 45;
10, 18, 24, 28, 30, 31, 34, 39, 46, 55;
11, 20, 27, 32, 35, 36, 38, 42, 48, 56, 66;
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..7260

Crossrefs

Cf. A000027 (left edge), A000217 (right edge), A000290 (central terms), A002717 (row sums); A220075.

Programs

Haskell

a220053 n k = a220053_tabl !! (n-1) !! (k-1)
a220053_row n = a220053_tabl !! (n-1)
a220053_tabl = map (scanl1 (+)) a130517_tabl
-- Reinhard Zumkeller, Dec 03 2012

Mathematica

T[n_, 1] := n;
T[n_, n_] := n-1;
T[n_, k_] := Abs[2k - n - If[2k <= n+1, 2, 1]];
row[n_] := Table[T[n, k], {k, 1, n}] // Accumulate;
Table[row[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Sep 23 2021 *)

Formula

T(n,k) = Sum_{i=1..k} A130517(n, i).