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 A165136 a(n) is the number of patterns for n-digit papaya numbers. 3
 1, 2, 4, 10, 21, 50, 99, 250, 454, 1242, 2223, 6394, 11389, 35002, 62034, 202010, 359483, 1233518, 2203507, 7944100, 14249715, 53810836, 96911168, 382258438, 691048071, 2840120987, 5152403569, 22010733048, 40059670261, 177444599715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Papaya numbers are concatenations of two palindromes or palindromes themselves (think of "papaya" as the concatenation of the palindromes "pap" and "aya"). The actual number of n-digit papaya numbers is A165135. If the pattern is "aa", for example, inserting digits 1 to 9 for "a" gives 9 positive 2-digit numbers, 11, 22, ...,99.The pattern "ab" inserting a<>b gives 10, 12,..,98, that is 9*9 = 81 positive 2-digit numbers.(9 different choices for "a" because leading 0's are not allowed, and for each "a" 9 different choices of "b".)So the a(2) =2 two different patterns represent 9+81= A165135(2) different 2-digit numbers. The first 19 terms of this sequence are the same as in A165137. Then the sequences start to differ, because the number of patterns in an infinite alphabet can be larger than patterns in the 10-digits-alphabet of ordinary numbers: A165137(20) = a(20)+10. [From Tanya Khovanova, Oct 01 2009] (Since at most 2 symbols in a papaya number can be present only once, to require 11 symbols takes a length of 2 + (11-2)*2 = 20. The 10 strings for A165137(20) not counted here are abcdefghijkjihgfedbc, abacdefghijkjihgfedc, abcbadefghijkjihgfed, ..., abcdefghijihgfedcbak. - Franklin T. Adams-Watters, Apr 10 2011. LINKS Tanya Khovanova, Papaya Words and Numbers FORMULA a(n) = R(n) - Sum_{d|n,d

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Last modified December 12 18:24 EST 2018. Contains 318081 sequences. (Running on oeis4.)