A206492 Sums of rows of the sequence of triangles with nonnegative integers and row widths defined by A004738.

0, 3, 3, 9, 21, 19, 11, 25, 45, 74, 66, 49, 26, 55, 90, 134, 190, 170, 138, 97, 50, 103, 162, 230, 310, 405, 365, 310, 243, 167, 85, 173, 267, 370, 485, 615, 763, 693, 605, 502, 387, 263, 133, 269, 411, 562, 725, 903, 1099, 1316, 1204, 1071, 920, 754, 576, 389

Offset: 1

Author

Alex Ratushnyak, Jun 28 2012

Keywords

• nonn
• easy

Comments

Row widths: A004738(n): 1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, 3, 4, 5...

Pits: A051925(n+1): 0, 3, 11, 26, 50, 85, 133, 196, 276, 375, 495, 638...

Peak tops: A007290(n+3): 2, 8, 20, 40, 70, 112, 168, 240, 330, 440, 572...

Peak bases: A084990(n+1): 1, 6, 17, 36, 65, 106, 161, 232, 321, 430, 561...

Examples

			The sequence of triangles begins:
0
1 2
3
4 5
6 7 8
9 10
11
12 13
14 15 16
17 18 19 20
21 22 23
24 25
26
27 28
29 30 31
32 33 34 35
36 37 38 39 40
41 42 43 44
45 46 47
48 49
50
51 52
		

Crossrefs

Cf. A004738, A051925, A007290, A084990.

Cf. A027480: sums of rows of a triangle with increasing row widths: 0; 1,2; 3,4,5; 6,7,8,9; ...

Programs

Python

curSign=-1
curLength=sum=0
rowLength=topLength=1
for n in range(1232):
    sum += n
    curLength += 1
    if curLength==rowLength:
        print(sum, end=',')
        curLength = sum = 0
        if rowLength==1 or rowLength==topLength:
            curSign = -curSign
        topLength += (rowLength==1)
        rowLength += curSign