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

1,2

Links

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

Formula

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

Example

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;

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A180986 A200763 A203291 * A320509 A358298 A347712

Adjacent sequences: A220050 A220051 A220052 * A220054 A220055 A220056

Keyword

nonn,tabl,easy

Author

Reinhard Zumkeller, Dec 03 2012

Status

approved