A220075 Partial sums in rows of A220073, triangle read by rows.

1, 1, 3, 2, 3, 6, 3, 4, 6, 10, 4, 6, 7, 10, 15, 5, 8, 9, 11, 15, 21, 6, 10, 12, 13, 16, 21, 28, 7, 12, 15, 16, 18, 22, 28, 36, 8, 14, 18, 20, 21, 24, 29, 36, 45, 9, 16, 21, 24, 25, 27, 31, 37, 45, 55, 10, 18, 24, 28, 30, 31, 34, 39, 46, 55, 66, 11, 20, 27

Offset: 1

Author

Reinhard Zumkeller, Dec 03 2012

Keywords

• nonn
• tabl

Comments

T(n,k) = sum(A220073(n,i): i=1..k).

Links

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

Crossrefs

Cf. A000027 (left edge), A000217 (right edge), A002061 (central terms), A019298 (row sums); A220053.

Programs

Haskell

a220075 n k = a220075_tabl !! (n-1) !! (k-1)
a220075_row n = a220075_tabl !! (n-1)
a220075_tabl = map (scanl1 (+)) a220073_tabl

Mathematica

A[n_, k_] := If[k == 1, n, If[k == n, n-1, Abs[2k-n-If[2k <= n+1, 2, 1]]]];
A220073[n_, k_] := A[n, n-k+1];
T[n_, k_] := Sum[A220073[n, i], {i, 1, k}];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 27 2021 *)