A272011 Irregular triangle read by rows: strictly decreasing sequences of nonnegative numbers given in lexicographic order.

0, 1, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 3, 3, 0, 3, 1, 3, 1, 0, 3, 2, 3, 2, 0, 3, 2, 1, 3, 2, 1, 0, 4, 4, 0, 4, 1, 4, 1, 0, 4, 2, 4, 2, 0, 4, 2, 1, 4, 2, 1, 0, 4, 3, 4, 3, 0, 4, 3, 1, 4, 3, 1, 0, 4, 3, 2, 4, 3, 2, 0, 4, 3, 2, 1, 4, 3, 2, 1, 0, 5, 5, 0, 5, 1, 5, 1

Offset: 0

Author

Peter Kagey, Apr 17 2016

Keywords

• nonn
• tabf

Comments

Length of n-th row given by A000120(n);

Maximum of n-th row given by A000523(n);

Minimum of n-th row given by A007814(n);

GCD of n-th row given by A064894(n);

Sum of n-th row given by A073642(n + 1).

n-th row begins at index A000788(n - 1) for n > 0.

The first appearance of n is at A001787(n).

a(A001787(n) + 1) = a(A001787(n)) for all n > 0.

a(A001787(n) + 2) = 0 for all n > 0.

a(A001787(n) + 3) = a(A001787(n)) for all n > 1.

a(A001787(n) + 4) = 1 for all n > 1.

a(A001787(n) + 5) = a(A001787(n)) for all n > 1.

Row n < 1024 lists the digits of A262557(n). - M. F. Hasler, Dec 11 2019

Examples

			Row n is given by the exponents in the binary expansion of n. For example, row 5 = [2, 0] because 5 = 2^2 + 2^0.
Row 0: []
Row 1: [0]
Row 2: [1]
Row 3: [1, 0]
Row 4: [2]
Row 5: [2, 0]
Row 6: [2, 1]
Row 7: [2, 1, 0]
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000120, A000523, A001787, A007814, A064894, A073642.

Cf. A133457 gives the rows in reverse order.

Cf. A272020, A262557.

Programs

Mathematica

Map[Length[#] - Flatten[Position[#, 1]] &, IntegerDigits[Range[50], 2]] (* Paolo Xausa, Feb 13 2024 *)

PARI

apply( A272011_row(n)=Vecrev(vecextract([0..exponent(n+!n)],n)), [0..39]) \\ For n < 2^10: row(n)=digits(A262557[n]). There are 2^k rows starting with k, they start at row 2^k. - M. F. Hasler, Dec 11 2019