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A272011 Irregular triangle read by rows: strictly decreasing sequences of nonnegative numbers given in lexicographic order. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
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
LINKS
EXAMPLE
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]
MATHEMATICA
Map[Length[#] - Flatten[Position[#, 1]] &, IntegerDigits[Range[50], 2]] (* Paolo Xausa, Feb 13 2024 *)
PROG
(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
CROSSREFS
Cf. A133457 gives the rows in reverse order.
Sequence in context: A319954 A050949 A074943 * A352362 A236374 A045719
KEYWORD
nonn,tabf,changed
AUTHOR
Peter Kagey, Apr 17 2016
STATUS
approved

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Last modified February 21 10:47 EST 2024. Contains 370228 sequences. (Running on oeis4.)