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 1-7 of 7 results.

A308926 Sum of all the parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 7, 8, 18, 30, 55, 84, 143, 210, 315, 448, 646, 882, 1235, 1640, 2205, 2882, 3772, 4824, 6200, 7800, 9828, 12208, 15138, 18540, 22723, 27520, 33297, 39950, 47845, 56844, 67488, 79534, 93600, 109520, 127920, 148638, 172473, 199144, 229590
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308927, A308928, A308929, A308930, A308931, A308932, A308933.

Programs

  • Mathematica
    Table[Total[Flatten[IntegerPartitions[n,{7}]]],{n,0,50}] (* Harvey P. Dale, Jul 27 2025 *)

Formula

a(n) = n * Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} 1.
a(n) = n * A026813(n).
a(n) = A308927(n) + A308928(n) + A308929(n) + A308930(n) + A308931(n) + A308932(n) + A308933(n).

A308927 Sum of the smallest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 22, 30, 41, 54, 72, 93, 121, 153, 194, 242, 302, 372, 457, 557, 675, 812, 975, 1162, 1381, 1632, 1924, 2254, 2636, 3068, 3562, 4119, 4752, 5463, 6265, 7162, 8170, 9293, 10549, 11942, 13496, 15211, 17115, 19214
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308928, A308929, A308930, A308931, A308932, A308933.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[o, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} o.
a(n) = A308926(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).

A308928 Sum of the sixth largest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 24, 33, 46, 61, 84, 109, 144, 184, 237, 298, 379, 470, 585, 719, 882, 1069, 1300, 1560, 1873, 2230, 2653, 3129, 3694, 4326, 5063, 5892, 6848, 7917, 9147, 10513, 12071, 13804, 15765, 17935, 20389, 23088, 26118
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308927, A308929, A308930, A308931, A308932, A308933.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[m, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} m.
a(n) = A308926(n) - A308927(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).

A308929 Sum of the fifth largest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 27, 38, 54, 73, 101, 133, 177, 230, 298, 380, 485, 608, 762, 944, 1165, 1423, 1738, 2101, 2534, 3035, 3625, 4300, 5095, 5996, 7043, 8231, 9598, 11142, 12910, 14893, 17148, 19674, 22529, 25709, 29295, 33267
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308930, A308931, A308932, A308933.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[l, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} l.
a(n) = A308926(n) - A308927(n) - A308928(n) - A308930(n) - A308931(n) - A308932(n) - A308933(n).

A308931 Sum of the third largest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 42, 61, 88, 121, 171, 228, 307, 405, 531, 682, 880, 1111, 1403, 1750, 2174, 2670, 3281, 3983, 4827, 5807, 6965, 8291, 9861, 11641, 13718, 16080, 18804, 21881, 25423, 29392, 33921, 39001, 44753, 51163, 58411
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308932, A308933.

Programs

  • Mathematica
    Table[Total[IntegerPartitions[n,{7}][[All,3]]],{n,0,50}] (* Harvey P. Dale, Aug 15 2020 *)

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} j.
a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308932(n) - A308933(n).

A308932 Sum of the second largest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 61, 87, 128, 175, 249, 331, 450, 590, 779, 998, 1292, 1628, 2063, 2567, 3198, 3923, 4827, 5854, 7106, 8538, 10253, 12197, 14516, 17126, 20197, 23658, 27683, 32197, 37422, 43247, 49931, 57382, 65865, 75275
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308931, A308933.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[i, {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} i.
a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308933(n).

A308933 Sum of the largest parts in the partitions of n into 7 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 69, 106, 153, 222, 307, 430, 577, 778, 1023, 1343, 1726, 2221, 2805, 3540, 4408, 5475, 6722, 8244, 10004, 12116, 14557, 17447, 20758, 24656, 29090, 34254, 40115, 46878, 54512, 63276, 73112, 84322, 96875, 111089
Offset: 0

Views

Author

Wesley Ivan Hurt, Jun 30 2019

Keywords

Links

Crossrefs

Cf. A026813, A308926, A308927, A308928, A308929, A308930, A308931, A308932.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[(n - i - j - k - l - m - o), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} (n-i-j-k-l-m-o).
a(n) = A308926(n) - A308927(n) - A308928(n) - A308929(n) - A308930(n) - A308931(n) - A308932(n).
Showing 1-7 of 7 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.