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

1,2

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...

Links

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

Example

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

Prog

(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

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; ...

Sequence in context: A099094 A222169 A222444 * A007683 A316220 A059728

Adjacent sequences: A206489 A206490 A206491 * A206493 A206494 A206495

Keyword

nonn,easy

Author

Alex Ratushnyak, Jun 28 2012

Status

approved