A195311 Row sums of A195310.

0, 1, 3, 5, 7, 10, 13, 17, 21, 25, 29, 33, 38, 43, 48, 54, 60, 66, 72, 78, 84, 90, 97, 104, 111, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 199, 208, 217, 226, 235, 245, 255, 265, 275, 285, 295, 305, 315, 325, 335, 345, 356, 367, 378, 389, 400

Offset

1,3

Links

Table of n, a(n) for n=1..56.

Example

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).
Triangle begins:
0,
1,3,5,
7,10,
13,17,21,25,29,
33,38,43,
48,54,60,66,72,78,84,
90,97,104,111,
118,126,134,142,150,158,166,174,182,
190,199,208,217,226,
235,245,255,265,275,285,295,305,315,325,335,
345,356,367,378,389,400

Mathematica

a1318[n_] := If[EvenQ[n], n (3 n/2 + 1)/4, (n + 1) (3 n + 1)/8];
a[n_] := DeleteCases[Table[n - a1318[k], {k, 1, n}], _?Negative] // Total;
Array[a, 56] (* Jean-François Alcover, Jun 26 2019 *)

Prog

(Sage)
def A195311(n):
    return add(max(0, n-k*(3*k-1)/2)+max(0, n-k*(3*k+1)/2) for k in (1..n))
[A195311(n) for n in (1..56)]  # Peter Luschny, Oct 12 2012

Crossrefs

Cf. A001318, A026741, A195309, A195310.

Sequence in context: A029899 A072166 A077000 * A184013 A057672 A112509

Adjacent sequences: A195308 A195309 A195310 * A195312 A195313 A195314

Keyword

nonn

Author

Omar E. Pol, Sep 21 2011

Status

approved