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A244232 Sum of "digit values" in Semigreedy Catalan Representation of n, A244159. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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.

Equivalent description: partition n "greedily" as terms of A197433, i.e. n = A197433(i) + A197433(j) + ... + A197433(k), always using the largest term of A197433 that still "fits in" (i.e. is <= n remaining). Then a(n) = A000120(i) + A000120(j) + ... + A000120(k).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16796

FORMULA

If A176137(n) = 1, a(n) = A000120(A244230(n)), otherwise a(n) = A000120(A244230(n)-1) + a(n-A197433(A244230(n)-1)).

For all n, a(A000108(n)) = 1. [And moreover, Catalan numbers, A000108, give all such k that a(k) = 1].

For all n, a(A014138(n)) = n and a(A014143(n)) = A000217(n+1).

EXAMPLE

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.

PROG

(Scheme, two alternative implementations)

;; One based on recurrence:

(definec (A244232 n) (if (not (zero? (A176137 n))) (A000120 (A244230 n)) (+ (A000120 (-1+ (A244230 n))) (A244232 (- n (A197433 (-1+ (A244230 n))))))))

;; Another using function A244159raw given in A244159:

(define (A244232 n) (apply + (vector->list (A244159raw n))))

CROSSREFS

Cf. A000108, A000120, A176137, A197433, A244230, A244159, A244231, A244233, A244234, A014420, A236855.

Sequence in context: A079087 A324920 A236855 * A227781 A254761 A227552

Adjacent sequences:  A244229 A244230 A244231 * A244233 A244234 A244235

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 25 2014

STATUS

approved

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Last modified September 18 03:39 EDT 2020. Contains 337164 sequences. (Running on oeis4.)