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A244232
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Sum of "digit values" in Semigreedy Catalan Representation of n, A244159.
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7
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0, 1, 1, 2, 3, 1, 2, 2, 3, 4, 4, 5, 6, 4, 1, 2, 2, 3, 4, 2, 3, 3, 4, 5, 5, 6, 7, 5, 6, 6, 7, 8, 8, 9, 10, 8, 5, 6, 6, 7, 8, 6, 1, 2, 2, 3, 4, 2, 3, 3, 4, 5, 5, 6, 7, 5, 2, 3, 3, 4, 5, 3, 4, 4, 5, 6, 6, 7, 8, 6, 7, 7, 8, 9, 9, 10, 11, 9, 6, 7, 7, 8, 9, 7, 8, 8, 9, 10, 10, 11, 12, 10, 11, 11, 12, 13, 13, 14, 15, 13, 10, 11, 11, 12, 13, 11, 6, 7, 7, 8, 9, 7, 8, 8, 9, 10, 10, 11, 12, 10, 7, 8, 8, 9, 10, 8, 9, 9, 10, 11, 11, 12, 1
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OFFSET
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0,4
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COMMENTS
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Note that a(33604) = A000217(10) = 55 because the sum is computed from the underlying list (vector) of numbers, and thus is not subject to any corruption by decimal representation as A244159 itself is.
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LINKS
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FORMULA
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For all n, a(A000108(n)) = 1. [And moreover, Catalan numbers, A000108, give all such k that a(k) = 1].
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EXAMPLE
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For n=18, using the alternative description, we see that it is partitioned into the terms of A197433 as a greedy sum A197433(11) + A197433(1) = 17 + 1. Thus a(18) = A000120(11) + A000120(1) = 3+1 = 4.
For n=128, we see that is likewise represented as A197433(31) + A197433(31) = 64 + 64. Thus a(128) = 2*A000120(31) = 10.
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PROG
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(Scheme, two alternative implementations)
;; One based on recurrence:
;; Another using function A244159raw given in A244159:
(define (A244232 n) (apply + (vector->list (A244159raw n))))
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CROSSREFS
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Cf. A000108, A000120, A176137, A197433, A244230, A244159, A244231, A244233, A244234, A014420, A236855.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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