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A272011
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Irregular triangle read by rows: strictly decreasing sequences of nonnegative numbers given in lexicographic order.
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14
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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
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OFFSET
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0,5
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COMMENTS
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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) + 2) = 0 for all n > 0.
a(A001787(n) + 4) = 1 for all n > 1.
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LINKS
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EXAMPLE
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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]
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MATHEMATICA
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Map[Length[#] - Flatten[Position[#, 1]] &, IntegerDigits[Range[50], 2]] (* Paolo Xausa, Feb 13 2024 *)
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PROG
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(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
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CROSSREFS
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Cf. A133457 gives the rows in reverse order.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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