A080310 -id:A080310 - cp's OEIS frontend

A080293 A014486-encoding of the branch-reduced binomial-mod-2 binary trees.

2, 50, 14642, 3969842, 267572689202, 69427226972978, 4581045692538239282, 301220569271221714981682, 1295918094920364850246919050705202, 332029112115571675270693117549056818

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

These are obtained from the stunted binomial-mod-2 zigzag trees (A080263) either by extending each leaf to a branch of two leaves, or by branch-reducing every other such tree.

a(n) = A014486(A080295(n)). Same sequence in binary: A080294. Breadth-first-wise encoding: A080318. "Moose-trees" obtained from these: A080973. Cf. A080292, A080297.

a(n) = A080310(A080263(n)) = A014486(A080298(A080265(n))) = A014486(A080979(A080265(2*n)))

A080298 Positions of A080299 in A014486.

Original entry on oeis.org

1, 6, 39, 53, 345, 359, 477, 491, 567, 3634, 3648, 3766, 3780, 3856, 5064, 5078, 5196, 5210, 5286, 6065, 6079, 6155, 6595, 42088, 42102, 42220, 42234, 42310, 43518, 43532, 43650, 43664, 43740, 44519, 44533, 44609, 45049, 58884, 58898, 59016

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

a(n) = A080300(A080299(n)).

a(n) = A080300(A080310(A014486(n)))

A080299 A014486-encoding of plane binary trees (Stanley's d) whose interior zigzag-tree (Stanley's c, i.e., tree obtained by discarding the outermost edges of the binary tree) is isomorphic to a valid plane binary tree (Stanley's d).

Original entry on oeis.org

2, 50, 818, 914, 13106, 13202, 14642, 14738, 15506, 209714, 209810, 211250, 211346, 212114, 234290, 234386, 235826, 235922, 236690, 248114, 248210, 248978, 255122, 3355442, 3355538, 3356978, 3357074, 3357842, 3380018, 3380114, 3381554

Offset: 0

Antti Karttunen, Mar 02 2003

nonn

These trees are obtained by replacing each non-root terminal node (a leaf) of the binary tree with a branch of two leaves, i.e., "." -> "\/".

A. Karttunen, Nine initial trees can be found here (The trees with the ordinal numbers 1., 6., 39., 53., 345., 359., 477., 491. and 567.)
R. P. Stanley, Exercises on Catalan and Related Numbers

a(n) = A014486(A080298(n)). Breadth-first-wise encoding: A080313.

a(n) = A080310(A014486(n)).

A080303 Rewrite 0->100 in the binary expansion of n.

Original entry on oeis.org

4, 1, 12, 3, 100, 25, 28, 7, 804, 201, 204, 51, 228, 57, 60, 15, 6436, 1609, 1612, 403, 1636, 409, 412, 103, 1828, 457, 460, 115, 484, 121, 124, 31, 51492, 12873, 12876, 3219, 12900, 3225, 3228, 807, 13092, 3273, 3276, 819, 3300, 825, 828, 207, 14628

Offset: 0

Antti Karttunen, Mar 02 2003

			2 = 10 in binary, is rewritten as 1100 so a(2)=12.
4 = 100 in binary, is rewritten as 1100100 which is 100 as decimal number, thus a(4)=100.
5 = 101 in binary, is rewritten as 11001, 25 in binary, thus a(5)=25.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A080310.

Table[FromDigits[Flatten[IntegerDigits[n,2]/.(0->{1,0,0})],2],{n,0,80}] (* Harvey P. Dale, Aug 19 2021 *)

(define (A080303 n) (cond ((zero? n) 4) ((= n 1) n) ((odd? n) (+ 1 (* 2 (A080303 (/ (- n 1) 2))))) (else (+ 4 (* 8 (A080303 (/ n 2)))))))

cp's OEIS Frontend

A080293 A014486-encoding of the branch-reduced binomial-mod-2 binary trees.

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A080298 Positions of A080299 in A014486.

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A080299 A014486-encoding of plane binary trees (Stanley's d) whose interior zigzag-tree (Stanley's c, i.e., tree obtained by discarding the outermost edges of the binary tree) is isomorphic to a valid plane binary tree (Stanley's d).

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A080303 Rewrite 0->100 in the binary expansion of n.

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