A330027 a(0) = 0; for n > 0, a(n) is the total number of repeated strings in the concatenation of terms a(0) to a(n-1). Repeated strings can overlap.

0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 12, 16, 18, 20, 22, 25, 28, 30, 32, 34, 38, 40, 42, 44, 47, 50, 52, 55, 59, 62, 64, 66, 69, 72, 74, 76, 79, 82, 85, 88, 91, 96, 99, 103, 112, 118, 125, 130, 134, 140, 144, 150, 155, 161, 168, 173, 177, 183, 188, 194, 199, 205, 210

Offset: 0

Author

Scott R. Shannon, Nov 27 2019

Keywords

• nonn
• base

Comments

This sequence uses the same rule as A330015 but, instead of the count of unique repeated strings, here the total number of repeated strings seen in the concatenation of a(0) to a(n-1) forms the next term. After a(19) all single digits have been seen, so from that entry all new terms increase the previous term by at least the number of digits in the previous term. In this sequence repeated strings can be overlapping, thus a new entry '444' would add at least two to the total repeated count if '44' was already in the sequence, or at least one otherwise as '444' contains a repeat of '44' itself.

Examples

			a(4) = 2 as both '0' and '1' have repeated in the terms a(0) to a(3).
a(21) = 12, as a(11) = 10 which added another appearance of '0' and '1', so the total repeated string count incremented by two.
a(22) = 16, as a(21) = 12 which added another appearance of '1','2','12','01', so the total repeated string count incremented by four.
		

Crossrefs

Cf. A225224, A329818, A329448, A330015, A327036.