

A064064


nth step is to add a(n) to each previous number a(k) (including itself, i.e., k <= n) to produce n+1 more terms of the sequence, starting with a(0)=1.


4



1, 2, 3, 4, 4, 5, 6, 5, 6, 7, 8, 5, 6, 7, 8, 8, 6, 7, 8, 9, 9, 10, 7, 8, 9, 10, 10, 11, 12, 6, 7, 8, 9, 9, 10, 11, 10, 7, 8, 9, 10, 10, 11, 12, 11, 12, 8, 9, 10, 11, 11, 12, 13, 12, 13, 14, 9, 10, 11, 12, 12, 13, 14, 13, 14, 15, 16, 6, 7, 8, 9, 9, 10, 11, 10, 11, 12, 13, 10, 7, 8, 9, 10, 10
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OFFSET

0,2


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000


FORMULA

a(0) = 1 and a(n+1) = a(A002262(n)) + a(A003056(n)) for any n >= 0.  Rémy Sigrist, Aug 07 2017


EXAMPLE

Start with (1). So after initial step we have (*1*, 1+1 = 2), then (1, *2*, 1+2 = 3, 2+2 = 4), then (1, 2, *3*, 4, 1+3 = 4, 2+3 = 5, 3+3 = 6), then (1, 2, 3, *4*, 4, 5, 6, 1+4 = 5, 2+4 = 6, 3+4 = 7, 4+4 = 8), then (1, 2, 3, 4, *4*, 5, 6, 5, 6, 7, 8, 1+4 = 5, 2+4 = 6, 3+4 = 7, 4+4 = 8, 4+4 = 8), etc.


PROG

(PARI) a(n) = if (n==0, return (1), return (a(A002262(n1))+a(A003056(n1)))) \\ Rémy Sigrist, Aug 07 2017


CROSSREFS

Each number eventually appears A001190 times (binary rooted trees can be constructed by combining earlier trees in a similar manner with the nth tree having a(n) end points). Cf. A064065, A064066, A064067.
Cf. A002262, A003056.
Sequence in context: A051898 A092032 A058222 * A101504 A125568 A248110
Adjacent sequences: A064061 A064062 A064063 * A064065 A064066 A064067


KEYWORD

nonn


AUTHOR

Henry Bottomley, Aug 31 2001


STATUS

approved



