cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A057517 Binary encodings of the Catalan mountain ranges with exactly one sea-level valley, i.e., the rooted plane trees with root degree = 2.

Original entry on oeis.org

10, 44, 50, 180, 184, 204, 210, 226, 724, 728, 740, 744, 752, 820, 824, 844, 850, 866, 908, 914, 930, 962, 2900, 2904, 2916, 2920, 2928, 2964, 2968, 2980, 2984, 2992, 3012, 3016, 3024, 3040, 3284, 3288, 3300, 3304, 3312, 3380, 3384, 3404, 3410, 3426
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2000

Keywords

Comments

This bijective mapping from all rooted plane trees to one node larger, root degree = 2 trees illustrates the fact that CONV(A000108, A000108) = LEFT(A000108). (Catalan numbers shift left under convolution).

Crossrefs

Cf. A057501 (for binexp2pars, pars2binexp, car, cdr), A057518, A057519, A057122. Single-trunked trees: A057547.

Programs

  • Maple
    alltrees2doubletrunked := n -> pars2binexp(alltrees2doubletrunkedP(binexp2pars(n)));
alltrees2doubletrunkedP := h -> [car(h),cdr(h)];

Formula

a(n) = alltrees2doubletrunked(A014486(n)) (Starting from n=1).

A057518 The global ranks of each term of A057517, i.e., tells that A057515(A057518(n)) = 2 for all n.

Original entry on oeis.org

2, 5, 6, 12, 13, 15, 16, 19, 31, 32, 34, 35, 36, 40, 41, 43, 44, 47, 52, 53, 56, 60, 87, 88, 90, 91, 92, 96, 97, 99, 100, 101, 103, 104, 105, 106, 115, 116, 118, 119, 120, 124, 125, 127, 128, 131, 136, 137, 140, 144, 152, 153, 155, 156, 159, 164, 165, 168, 172, 178
Offset: 1

Views

Author

Antti Karttunen, Sep 03 2000

Keywords

Crossrefs

Cf. A057517, A057519.

Programs

  • Maple
    map(CatalanRankGlobal, A057517); # CatalanRankGlobal given in A057117.

A057549 The local ranks of each term of A057547.

Original entry on oeis.org

0, 1, 3, 4, 8, 9, 11, 12, 13, 22, 23, 25, 26, 27, 31, 32, 34, 35, 36, 38, 39, 40, 41, 64, 65, 67, 68, 69, 73, 74, 76, 77, 78, 80, 81, 82, 83, 92, 93, 95, 96, 97, 101, 102, 104, 105, 106, 108, 109, 110, 111, 115, 116, 118, 119, 120, 122, 123, 124, 125, 127, 128, 129
Offset: 0

Views

Author

Antti Karttunen, Sep 07 2000

Keywords

Crossrefs

Cf. A057519, A057548, A057550.

Formula

a(n) = CatalanRank(floor(binwidth(A057547[n])/2), A057547[n])
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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