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.

Previous Showing 11-20 of 24 results. Next

A326464 Sum of all the parts in the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 22, 36, 65, 98, 165, 240, 374, 540, 779, 1080, 1533, 2068, 2829, 3768, 5025, 6552, 8586, 11004, 14152, 17940, 22692, 28384, 35508, 43894, 54215, 66420, 81178, 98496, 119340, 143560, 172446, 205968, 245444, 291060, 344565
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 07 2019

Keywords

Links

Crossrefs

Cf. A026815, A326465, A326466, A326467, A326468, A326469, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[n * Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = n * Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} 1.
a(n) = A326465(n) + A326466(n) + A326467(n) + A326468(n) + A326469(n) + A326470(n) + A326471(n) + A326472(n) + A326473(n).

A326465 Sum of the smallest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 31, 42, 56, 76, 99, 130, 168, 216, 274, 349, 435, 544, 674, 831, 1017, 1244, 1507, 1823, 2194, 2629, 3136, 3734, 4420, 5223, 6148, 7215, 8438, 9851, 11453, 13292, 15382, 17758, 20447, 23502, 26935
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 07 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326466, A326467, A326468, A326469, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Total[Last/@IntegerPartitions[n,{9}]],{n,0,60}] (* Harvey P. Dale, Sep 13 2019 *)

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} q.
a(n) = A326464(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

A326466 Sum of the eighth largest parts in the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 23, 32, 44, 59, 81, 106, 141, 183, 239, 305, 392, 492, 622, 775, 965, 1189, 1468, 1790, 2184, 2644, 3195, 3835, 4600, 5479, 6523, 7722, 9125, 10733, 12611, 14744, 17218, 20030, 23264, 26925, 31120, 35845
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326467, A326468, A326469, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[p, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} p.
a(n) = A326464(n) - A326465(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

A326467 Sum of the seventh largest parts in the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 34, 47, 64, 88, 117, 157, 206, 271, 349, 451, 572, 727, 914, 1145, 1422, 1764, 2167, 2657, 3237, 3932, 4747, 5720, 6851, 8191, 9744, 11563, 13664, 16115, 18924, 22179, 25904, 30190, 35071, 40666, 47006
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326468, A326469, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} o.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

A326468 Sum of the sixth largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 26, 37, 52, 71, 100, 133, 181, 239, 317, 410, 536, 682, 874, 1104, 1392, 1735, 2167, 2670, 3292, 4025, 4911, 5947, 7199, 8645, 10375, 12377, 14736, 17456, 20654, 24307, 28569, 33441, 39071, 45478, 52862
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326469, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} m.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

A326469 Sum of the fifth largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 29, 42, 60, 83, 117, 158, 216, 288, 383, 500, 655, 840, 1080, 1371, 1734, 2172, 2718, 3364, 4157, 5099, 6235, 7574, 9184, 11059, 13294, 15895, 18955, 22501, 26657, 31432, 36991, 43368, 50731, 59138, 68811
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326470, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[l, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]
Table[Total[IntegerPartitions[n,{9}][[All,-5]]],{n,0,60}] (* Harvey P. Dale, Nov 07 2020 *)

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} l.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

A326470 Sum of the fourth largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 9, 15, 22, 35, 50, 73, 101, 145, 196, 270, 360, 484, 632, 832, 1069, 1382, 1755, 2229, 2794, 3508, 4346, 5384, 6608, 8101, 9847, 11960, 14413, 17354, 20760, 24791, 29444, 34923, 41201, 48535, 56926, 66654, 77731
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326471, A326472, A326473.

Programs

  • Mathematica
    Table[Total[IntegerPartitions[n,{9}][[;;,4]]],{n,0,50}] (* Harvey P. Dale, May 01 2023 *)

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} k.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326471(n) - A326472(n) - A326473(n).

A326471 Sum of the third largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 65, 94, 132, 190, 258, 355, 478, 640, 840, 1107, 1426, 1842, 2348, 2979, 3742, 4699, 5828, 7219, 8875, 10874, 13231, 16072, 19380, 23330, 27932, 33347, 39626, 46999, 55465, 65332, 76659, 89742, 104684
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326470, A326472, A326473.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[j, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} j.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326472(n) - A326473(n).

A326472 Sum of the second largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 91, 135, 188, 272, 368, 510, 682, 918, 1201, 1586, 2039, 2639, 3354, 4264, 5346, 6716, 8319, 10312, 12657, 15516, 18858, 22908, 27599, 33226, 39740, 47449, 56338, 66809, 78792, 92799, 108810, 127365
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326470, A326471, A326473.

Programs

  • Mathematica
    Table[Total[IntegerPartitions[n,{9}][[;;,2]]],{n,0,50}] (* Harvey P. Dale, Dec 03 2023 *)

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} i.
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326473(n).

A326473 Sum of the largest parts of the partitions of n into 9 parts.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 69, 108, 158, 232, 326, 464, 633, 869, 1164, 1557, 2041, 2678, 3449, 4442, 5645, 7153, 8967, 11224, 13903, 17187, 21081, 25785, 31321, 37963, 45714, 54930, 65650, 78263, 92860, 109946, 129586, 152417, 178584
Offset: 0

Views

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

Links

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326470, A326471, A326472.

Programs

  • Mathematica
    Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o-p-q), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (n-i-j-k-l-m-o-p-q).
a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n).
Previous Showing 11-20 of 24 results. Next

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

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