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A165135 The number of n-digit positive papaya numbers. 6
9, 90, 252, 1872, 4464, 29250, 62946, 393912, 809442, 4945140, 9899910, 59366286, 116999892, 692936460, 1349989992, 7919601912, 15299999856, 89099130960, 170999999838, 989995038012, 1889999872488, 10889990099100, 20699999999802, 118799939782206, 224999999981964 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Papaya numbers are concatenations of two palindromes or palindromes themselves. All one-digit and two-digit numbers are papaya numbers.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Tanya Khovanova, Papaya Words and Numbers

FORMULA

a(n) = A052268(n)-A165611(n). - R. J. Mathar, Sep 25 2009

a(n) = 9*R(n,10)/10 - Sum_{d|n,d<n} phi(n/d)*a(d) where R(2*k,r)=k*(r+1)*r^k, R(2*k+1,r)=(2*k+1)*r^(k+1). - Andrew Howroyd, Mar 29 2016

EXAMPLE

Three-digit papaya numbers are of four types: aaa (total of 9) and aab, aba, abb, (total of 81 for each). Hence a(3) = 252.

PROG

(PARI)

R(n, b)=if(n%2==0, n/2*(b+1)*b^(n/2), n*b^((n+1)/2));

a(n) = 9*R(n, 10)/10 - sumdiv(n, d, if(n<>d, eulerphi(n/d)*a(d))); \\ Andrew Howroyd, Oct 14 2017

CROSSREFS

Cf. A007055, A052268, A165610, A165611.

Sequence in context: A140160 A043960 A044641 * A277105 A180289 A210088

Adjacent sequences:  A165132 A165133 A165134 * A165136 A165137 A165138

KEYWORD

base,nonn

AUTHOR

Sergei Bernstein and Tanya Khovanova, Sep 04 2009

EXTENSIONS

a(7)-a(8) from R. J. Mathar, Sep 25 2009

a(9)-a(25) from Andrew Howroyd, Mar 29 2016

STATUS

approved

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Last modified December 13 08:08 EST 2018. Contains 318082 sequences. (Running on oeis4.)