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 1-6 of 6 results.

A064105 2nd column of 3rd-order Zeckendorf array A136189.

Original entry on oeis.org

2, 8, 11, 15, 21, 27, 30, 36, 39, 43, 49, 52, 56, 62, 68, 71, 75, 81, 87, 90, 96, 99, 103, 109, 115, 118, 124, 127, 131, 137, 140, 144, 150, 156, 159, 165, 168, 172, 178, 181, 185, 191, 197, 200, 204, 210, 216, 219, 225, 228, 232, 238, 241, 245, 251
Offset: 1

Views

Author

Naohiro Nomoto, Sep 17 2001

Keywords

Links

Crossrefs

Cf. A020942, A064106, A136189.

Formula

Any number n has a unique representation as a sum of terms from {2, 3, 4, 6, 9, 13, 19, ...} (cf. A000930) such that no two terms are adjacent or pen-adjacent; e.g. 8=6+2. Sequence gives all n where that representation involves 2.
a(n) = A020942(n) + A136495(n). - Alan Michael Gómez Calderón, Dec 21 2024
a(n) = A381841(n) - 1. - Jeffrey Shallit, Mar 08 2025

Extensions

Offset corrected by N. J. A. Sloane, Apr 29 2024

A372749 4th column of the 3-Zeckendorf array (A136189).

Original entry on oeis.org

4, 17, 23, 32, 45, 58, 64, 77, 83, 92, 105, 111, 120, 133, 146, 152, 161, 174, 187, 193, 206, 212, 221, 234, 247, 253, 266, 272, 281, 294, 300, 309, 322, 335, 341, 354, 360, 369, 382, 388, 397, 410, 423, 429, 438, 451, 464, 470, 483, 489, 498, 511, 517, 526, 539
Offset: 1

Views

Author

A.H.M. Smeets, May 12 2024

Keywords

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

Crossrefs

Cf. A000930, A136189, A350215.
The k-th row: A000930(n+2) (k=1)
The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), this sequence (k=4), A372750 (k=5).
The k-th prepended column: A005374 (k=1), A202342 (k=4)

Formula

a(n) = A202342(n) + A136496(n) + A381841(n) - 2. - Jeffrey Shallit, Mar 08 2025

A372750 5th column of the 3-Zeckendorf array (A136189).

Original entry on oeis.org

6, 25, 34, 47, 66, 85, 94, 113, 122, 135, 154, 163, 176, 195, 214, 223, 236, 255, 274, 283, 302, 311, 324, 343, 362, 371, 390, 399, 412, 431, 440, 453, 472, 491, 500, 519, 528, 541, 560, 569, 582, 601, 620, 629, 642, 661, 680, 689, 708, 717, 730, 749, 758, 771
Offset: 1

Views

Author

A.H.M. Smeets, May 12 2024

Keywords

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

Crossrefs

Cf. A000930, A136189, A350215.
The k-th row: A000930(n+2) (k=1)
The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), A372749 (k=4), this sequence (k=5).
The k-th prepended column: A005374 (k=1), A202342 (k=4)

Formula

a(n) = A202342(n) + A136496(n) + 2*A381841(n) - 3. - Jeffrey Shallit, Mar 08 2025

A372752 6th column of the 3-Zeckendorf array (A136189).

Original entry on oeis.org

9, 37, 50, 69, 97, 125, 138, 166, 179, 198, 226, 239, 258, 286, 314, 327, 346, 374, 402, 415, 443, 456, 475, 503, 531, 544, 572, 585, 604, 632, 645, 664, 692, 720, 733, 761, 774, 793, 821, 834, 853, 881, 909, 922, 941, 969, 997, 1010, 1038, 1051, 1070, 1098
Offset: 1

Views

Author

A.H.M. Smeets, May 12 2024

Keywords

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

Crossrefs

Cf. A000930, A136189, A350215.
The k-th row: A000930(n+2) (k=1)
The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), A372749 (k=4), A372750 (k=5), this sequence (k=6).
The k-th prepended column: A005374 (k=1), A202342 (k=4)

Formula

a(n) = 2*A202342(n) + A136496(n) + 3*A381841(n) - 4. - Jeffrey Shallit, Mar 08 2025

A372756 7th column of the 3-Zeckendorf array (A136189).

Original entry on oeis.org

13, 54, 73, 101, 142, 183, 202, 243, 262, 290, 331, 350, 378, 419, 460, 479, 507, 548, 589, 608, 649, 668, 696, 737, 778, 797, 838, 857, 885, 926, 945, 973, 1014, 1055, 1074, 1115, 1134, 1162, 1203, 1222, 1250, 1291, 1332, 1351, 1379, 1420, 1461, 1480, 1521
Offset: 1

Views

Author

A.H.M. Smeets, May 12 2024

Keywords

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

Crossrefs

Cf. A000930, A136189, A350215.
The k-th row: A000930(n+2) (k=1), A372760 (k=2).
The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), A372749 (k=4), A372750 (k=5), A372752 (k=6), this sequence (k=7), A372757 (k=8).
The k-th prepended column: A005374 (k=1), A136495 (k=2), A023443 (k=3), A202342 (k=4), A372758 (k=5), A372759 (k=6).

Formula

a(n) = 3*A202342(n) + 2*A136496(n) + 4*A381841(n) - 6. - Jeffrey Shallit, Mar 08 2025

A372757 8th column of the 3-Zeckendorf array (A136189).

Original entry on oeis.org

19, 79, 107, 148, 208, 268, 296, 356, 384, 425, 485, 513, 554, 614, 674, 702, 743, 803, 863, 891, 951, 979, 1020, 1080, 1140, 1168, 1228, 1256, 1297, 1357, 1385, 1426, 1486, 1546, 1574, 1634, 1662, 1703, 1763, 1791, 1832, 1892, 1952, 1980, 2021, 2081, 2141
Offset: 1

Views

Author

A.H.M. Smeets, May 12 2024

Keywords

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

Crossrefs

Cf. A000930, A136189, A350215.
The k-th row: A000930(n+2) (k=1), A372760 (k=2).
The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), A372749 (k=4), A372750 (k=5), A372752 (k=6), A372756 (k=7), this sequence (k=8).
The k-th prepended column: A005374 (k=1), A136495 (k=2), A023443 (k=3), A202342 (k=4), A372758 (k=5), A372759 (k=6).

Formula

a(n) = 4*A202342(n) + 3*A136496(n) + 6*A381841(n) - 9. - Jeffrey Shallit, Mar 08 2025
Showing 1-6 of 6 results.

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

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