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A295508 Triangle read by rows, related to binary partitions of n. 2
0, 1, 0, 2, 1, 0, 3, 2, 1, 4, 3, 2, 0, 5, 4, 3, 1, 6, 5, 4, 2, 7, 6, 5, 3, 8, 7, 6, 4, 0, 9, 8, 7, 5, 1, 10, 9, 8, 6, 2, 11, 10, 9, 7, 3, 12, 11, 10, 8, 4, 13, 12, 11, 9, 5, 14, 13, 12, 10, 6, 15, 14, 13, 11, 7, 16, 15, 14, 12, 8, 0, 17, 16, 15, 13, 9, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..76.

FORMULA

Let L(n) = (length of binary representation of n) - 0^n then

T(n, k) = n if k=0 else n - 2^(k-1) for n >= 0 and 0 <= k <= L(n).

Sum_{k=0..L(n)} T(n,k) = A123753(n-1) for n>=1.

EXAMPLE

0;

1,   0;

2,   1,  0;

3,   2,  1;

4,   3,  2,  0;

5,   4,  3,  1;

6,   5,  4,  2;

7,   6,  5,  3;

8,   7,  6,  4, 0;

9,   8,  7,  5, 1;

10,  9,  8,  6, 2;

11, 10,  9,  7, 3;

12, 11, 10,  8, 4;

13, 12, 11,  9, 5;

14, 13, 12, 10, 6;

15, 14, 13, 11, 7;

MAPLE

A295508_row := proc(n) local i, s, z; s := n; i := n-1; z := 1;

while 0 <= i do s := s, i; i := i-z; z := z+z od; s end:

seq(A295508_row(n), n=0..17);

# Alternatively after formula:

T := (n, k) -> `if`(k=0, n, n - 2^(k-1)):

L := n -> nops(convert(n, base, 2)) - 0^n:

T_row := n -> seq(T(n, k), k=0..L(n)):

seq(T_row(n), n=0..17);

CROSSREFS

Cf. A123753.

Sequence in context: A019586 A257962 A176095 * A260672 A063942 A263405

Adjacent sequences:  A295505 A295506 A295507 * A295509 A295510 A295511

KEYWORD

nonn,tabf

AUTHOR

Peter Luschny, Nov 30 2017

STATUS

approved

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Last modified October 20 22:38 EDT 2018. Contains 316404 sequences. (Running on oeis4.)