A025581vs A122200 - very few differences (and very consistent pattern in those differences)

[Alexander Povolotsky]

It looks that A025581 & A122200 have very few differences (and very
consistent pattern exists in those differences) ?

Anybody has an explanation for that ?

Alex P.

A025581
Triangle T(n,k) = n-k, n >= 0, 0<=k<=k. Integers m to 0 followed by
integers m+1 to 0 etc.

0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5,
4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9,
8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10,
9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,
0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3 (list; table; graph; listen)
OFFSET

0,4

FORMULA

a(n) = (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) # Cf. A002262

G.f.: y / [(1-x)^2 * (1-xy) ]. - R. Stephan, Jan 25 2005

MAPLE

A025581 := n -> binomial(1+floor((1/2)+sqrt(2*(1+n))), 2) - (n+1);

PROGRAM

(PARI) a(n)=binomial(1+floor(1/2+sqrt(2+2*n)), 2)-(n+1) /* produces a(n) */

(PARI) t1(n)=binomial(floor(3/2+sqrt(2+2*n)), 2)-(n+1) /* A025581 */

(PARI) t2(n)=n-binomial(floor(1/2+sqrt(2+2*n)), 2) /* A002262 */

CROSSREFS

A004736(n+1)=1+A025581(n)

AUTHOR

David W. Wilson (davidwwilson(AT)comcast.net)

A122200
Signature permutations of RIBS-transformations of non-recursive
Catalan automorphisms in table A089840.

0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5,
4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 6, 5, 4, 3, 2, 1, 0, 9,
7, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10,
9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1,
0, 13, 13, 11, 10, 9, 8 (list; table; graph; listen)
OFFSET

0,4


CROSSREFS

Row 0 (identity permutation): A001477, row 1: A122282. See also tables
A089840, A122201-A122204, A122283-A122284, A122285-A122288,
A122289-A122290.

Adjacent sequences: A122197 A122198 A122199 this_sequence A122201
A122202 A122203

Sequence in context: A025677 A025651 A025670 this_sequence A025646
A025661 A025671



AUTHOR

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Sep 01 2006