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.

A340247 Sum of the third largest parts r of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 3, 5, 7, 10, 15, 19, 28, 33, 46, 57, 75, 84, 113, 129, 164, 184, 232, 256, 319, 347, 425, 466, 561, 601, 723, 777, 918, 981, 1152, 1224, 1428, 1509, 1746, 1849, 2122, 2227, 2550, 2678, 3040, 3184, 3600, 3760, 4234, 4410, 4942, 5151, 5745, 5961, 6635
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 01 2021

Keywords

Crossrefs

Cf. A062890, A340246, A340248, A340249.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[j*Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign(floor((i+k+j)/(n-i-j-k+1))) * j.

A340248 Sum of the second largest parts s of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

Original entry on oeis.org

0, 0, 0, 1, 1, 2, 4, 7, 10, 15, 22, 29, 42, 51, 71, 87, 116, 132, 177, 201, 259, 289, 368, 404, 508, 550, 681, 738, 900, 959, 1164, 1239, 1482, 1569, 1863, 1962, 2313, 2424, 2835, 2971, 3448, 3590, 4150, 4318, 4954, 5142, 5872, 6080, 6912, 7140, 8078, 8343, 9395, 9672
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 01 2021

Keywords

Crossrefs

Cf. A062890, A340246, A340247, A340249.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[i*Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j,  Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign(floor((i+k+j)/(n-i-j-k+1))) * i.

A340249 Sum of the largest parts t of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

Original entry on oeis.org

0, 0, 0, 1, 2, 2, 5, 8, 14, 18, 30, 35, 56, 63, 95, 109, 156, 166, 235, 255, 346, 369, 491, 517, 676, 707, 907, 952, 1200, 1239, 1548, 1605, 1974, 2037, 2481, 2550, 3078, 3156, 3774, 3874, 4592, 4685, 5522, 5642, 6596, 6726, 7818, 7958, 9200, 9354, 10754, 10939, 12510
Offset: 1

Views

Author

Wesley Ivan Hurt, Jan 01 2021

Keywords

Crossrefs

Cf. A062890, A340246, A340247, A340248.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[(n - i - j - k) Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign(floor((i+k+j)/(n-i-j-k+1))) * (n-i-j-k).
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.