A227752 a(n) is the number of occurrences of n in A226062.

1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 3, 1, 0, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0

Offset

0,7

Links

Antti Karttunen, Table of n, a(n) for n = 0..319

Formula

In the following formula [] stands for Iverson brackets. Essentially we are just naively counting the integers which A226062 maps to n. A000225 is the guaranteed upper limit for the runlength codes for the partitions of size n:

a(n) = Sum_{i=0..A000225(A227183(n))} [A226062(i)==n].

a(n) = Sum_{i=A227368(A227183(n))..A000225(A227183(n))} [A226062(i)==n]. [This is slightly faster if somebody invents a clever formula for the lower limit A227368.]

Prog

(Scheme, a naive implementation which always begins search from zero)
(definec (A227752 n) (add (lambda (k) (if (= n (A226062 k)) 1 0)) 0 (A000225 (A227183 n))))
;; The following function implements sum_{i=lowlim..uplim} intfun(i)
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))

Crossrefs

A227753 gives the positions of zeros.

Sequence in context: A278839 A348653 A278287 * A316771 A306269 A035212

Adjacent sequences: A227749 A227750 A227751 * A227753 A227754 A227755

Keyword

nonn

Author

Antti Karttunen, Jul 26 2013

Status

approved