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 1-4 of 4 results.

A062684 Number of addition triangles with apex n (version 1).

Original entry on oeis.org

1, 2, 3, 5, 7, 10, 13, 18, 23, 29, 37, 46, 55, 68, 81, 96, 115, 135, 155, 183, 211, 241, 277, 317, 357, 407, 457, 513, 577, 645, 713, 799, 885, 977, 1079, 1191, 1305, 1438, 1571, 1717, 1875, 2048, 2221, 2423, 2625, 2840, 3077, 3333, 3589, 3876, 4163
Offset: 1

Views

Author

Naohiro Nomoto, Feb 11 2002

Keywords

Comments

An addition triangle has any set of positive numbers as base; other rows are formed by adding pairs of adjacent numbers.
Reversing the base counts as a different triangle.

Examples

			For n = 5:
    5       5
   2,3     3,2     5     5     5     5
  1,1,2   2,1,1   4,1   1,4   2,3   3,2   5
with seven different bases, so a(5) = 7.

Links

Crossrefs

Cf. A028307, A066411, see A062896 for version 2.

Extensions

Extended and edited by John W. Layman, Feb 14 2002

A062896 Number of addition triangles with apex n (version 2).

Original entry on oeis.org

1, 2, 2, 4, 4, 7, 7, 12, 12, 18, 19, 27, 28, 39, 41, 54, 58, 74, 78, 99, 106, 129, 139, 168, 179, 214, 229, 268, 289, 335, 357, 414, 443, 504, 540, 612, 653, 737, 786, 878, 938, 1045, 1111, 1234, 1313, 1444, 1539, 1692, 1795, 1965, 2082, 2273, 2414
Offset: 1

Views

Author

Naohiro Nomoto, Feb 11 2002

Keywords

Comments

An addition triangle has any set of positive numbers as base; other rows are formed by adding pairs of adjacent numbers.
Reversing the base does not count as a different triangle.

Examples

			For n = 5:
    5
   2,3     5     5
  1,1,2   4,1   2,3   5.
with four different bases, so a(5) = 4.

Links

Crossrefs

See A062684 for version 1 (counts reversals).
Equivalent sequences with restrictions on rows: A337765 (weakly increasing), A337766 (strongly increasing).
Equivalent sequence where n is the sum of all numbers in the triangle: A337787.
Cf. A028307, A066411.

Extensions

Extended and edited by John W. Layman, Feb 14 2002

A346523 Number of sum pyramids for n.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 9, 11, 11, 18, 17, 22, 23, 29, 31, 38, 37, 46, 49, 58, 59, 72, 76, 86, 90, 106, 115, 131, 140, 159, 177, 189, 204, 236, 254, 274, 292, 328, 355, 398, 404, 455, 485, 518, 555, 622, 647, 698, 727, 808, 837, 922, 939, 1032, 1100
Offset: 1

Views

Author

J. Stauduhar, Jul 21 2021

Keywords

Comments

A sum pyramid for n is defined to be a pyramid with n at its apex, all pairs of adjacent members (x, y) of rows 2,3,4,... sum to the element immediately above, every element is positive and distinct, rows are complete (length of row m = length of row (m-1) + 1), reflections are not counted, and the pyramid is maximal (i.e., not part of a larger pyramid that qualifies). An example of the meaning of "maximal" can be seen in the Example section: the pyramids
.
9 9
6 3 and 5 4
.
are not counted because they consist of the top 2 rows of larger (3-row) pyramids that are counted. [Clarified by Peter Munn, Nov 20 2021]

Examples

			The five pyramids for a(9) are:
                9       9       9
   9     9     6 3     6 3     5 4
  8 1   7 2   5 1 2   4 2 1   2 3 1

Links

Crossrefs

Cf. A028307 (record pyramid heights), A337766, A348850.

Programs

  • Python
    See Links section.

Extensions

Definition aligned with A028307 by Peter Munn, Nov 20 2021

A028308 Form a triangle with n numbers in top row; all other numbers are the product of their parents. The numbers must be positive and distinct and the final number is to be minimized.

Original entry on oeis.org

1, 6, 48, 4320, 46448640, 10835538739200000, 2672817951712314077919313920000000
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

The next term has 69 digits. - Charlie Neder, Mar 09 2019

Examples

			Solutions for n=1,2,... are 1; 2 3; 3 2 4; 4 2 3 5; 5 3 2 4 7
Example triangle for a(4):
   4    2    3    5
     8    6    15
       48    90
         4320
Some solutions for a(6) and a(7) are (7,4,3,2,5,8) and (9,7,4,2,3,5,10), and others can be created by interchanging opposite numbers (e.g., swapping 5 and 7 in the second set). - _Charlie Neder_, Mar 09 2019

Links

Crossrefs

A less interesting cousin of A028307.

Extensions

a(7) and example removed from title by Charlie Neder, Mar 09 2019
Showing 1-4 of 4 results.

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

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