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 21-30 of 33 results. Next

A333486 Length of the n-th reversed integer partition in graded reverse-lexicographic order. Partition lengths of A228531.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 3, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 4, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 7, 1, 2, 2, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 6, 7, 8, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 7, 8, 9
Offset: 0

Views

Author

Gus Wiseman, May 23 2020

Keywords

Examples

			Triangle begins:
  0
  1
  1 2
  1 2 3
  1 2 2 3 4
  1 2 2 3 3 4 5
  1 2 2 3 2 3 3 4 4 5 6
  1 2 2 3 2 3 3 4 3 4 4 5 5 6 7
  1 2 2 2 3 3 4 2 3 3 4 3 4 4 5 4 5 5 6 6 7 8

Links

Crossrefs

Row lengths are A000041.
The generalization to compositions is A000120.
Row sums are A006128.
The same partition has sum A036042.
The length-sensitive version (sum/length/revlex) is A036043.
The colexicographic version (sum/colex) is A049085.
The same partition has minimum A182715.
The lexicographic version (sum/lex) is A193173.
The tetrangle of these partitions is A228531.
The version for non-reversed partitions is A238966.
The same partition has Heinz number A334436.
Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036.
Partitions in lexicographic order (sum/lex) are A193073.
Partitions in colexicographic order (sum/colex) are A211992.
Partitions in opposite Abramowitz-Stegun order (sum/length/revlex) are A334439.
Cf. A026792, A049085, A080576, A080577, A103921, A112798, A115623, A129129, A331581, A334302, A334435, A334442.

Programs

  • Mathematica
    revlexsort[f_,c_]:=OrderedQ[PadRight[{c,f}]];
Table[Length/@Sort[Reverse/@IntegerPartitions[n],revlexsort],{n,0,8}]

A333483 Sort all positive integers, first by sum of prime indices (A056239), then by number of prime indices (A001222).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 16, 11, 14, 15, 18, 20, 24, 32, 13, 21, 22, 25, 27, 28, 30, 36, 40, 48, 64, 17, 26, 33, 35, 42, 44, 45, 50, 54, 56, 60, 72, 80, 96, 128, 19, 34, 39, 49, 55, 52, 63, 66, 70, 75, 81, 84, 88, 90, 100, 108, 112, 120, 144, 160, 192, 256, 23, 38, 51, 65, 77, 68, 78, 98, 99, 105, 110, 125, 104, 126, 132, 135, 140, 150, 162, 168, 176, 180, 200, 216, 224, 240, 288, 320, 384, 512
Offset: 0

Views

Author

Gus Wiseman, May 10 2020

Keywords

Comments

A refinement of A215366, from which it first differs at a(49) = 55, A215366(49) = 52.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Examples

			Triangle begins:
   1
   2
   3   4
   5   6   8
   7   9  10  12  16
  11  14  15  18  20  24  32
  13  21  22  25  27  28  30  36  40  48  64
  17  26  33  35  42  44  45  50  54  56  60  72  80  96 128

Links

Crossrefs

Row lengths are A000041.
Ignoring length gives A215366 (graded Heinz numbers).
Sorting by decreasing length gives A333484.
Finally sorting lexicographically by prime indices gives A185974.
Finally sorting colexicographically by prime indices gives A334433.
Finally sorting reverse-lexicographically by prime indices gives A334435.
Finally sorting reverse-colexicographically by prime indices gives A334438.
Number of prime indices is A001222.
Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036.
Partitions in (sum/length/colex) order are A036037.
Sum of prime indices is A056239.
Sorting reversed partitions by Heinz number gives A112798.
Sorting partitions by Heinz number gives A296150.
Cf. A026791, A124734, A129129, A193073, A211992, A228100, A333219, A334301, A334434, A334439, A334441, A334442.

Programs

  • Mathematica
    Join@@@Table[Sort[Times@@Prime/@#&/@IntegerPartitions[n,{k}]],{n,0,8},{k,0,n}]

A344089 Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.

Original entry on oeis.org

1, 2, 3, 1, 2, 4, 1, 3, 5, 2, 3, 1, 4, 6, 2, 4, 1, 5, 1, 2, 3, 7, 3, 4, 2, 5, 1, 6, 1, 2, 4, 8, 3, 5, 2, 6, 1, 7, 1, 3, 4, 1, 2, 5, 9, 4, 5, 3, 6, 2, 7, 1, 8, 2, 3, 4, 1, 3, 5, 1, 2, 6, 10, 4, 6, 3, 7, 2, 8, 1, 9, 2, 3, 5, 1, 4, 5, 1, 3, 6, 1, 2, 7, 1, 2, 3, 4
Offset: 0

Views

Author

Gus Wiseman, May 12 2021

Keywords

Comments

First differs from the revlex (instead of colex) version for partitions of 12.
The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)
  3: (3)(12)
  4: (4)(13)
  5: (5)(23)(14)
  6: (6)(24)(15)(123)
  7: (7)(34)(25)(16)(124)
  8: (8)(35)(26)(17)(134)(125)
  9: (9)(45)(36)(27)(18)(234)(135)(126)

Links

Crossrefs

Positions of first appearances are A015724 plus one.
Taking lex instead of colex gives A026793 (non-reversed: A118457).
Triangle sums are A066189.
Reversing all partitions gives A344090.
The non-strict version is A344091.
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
Cf. A005117, A014466, A209862, A325683, A325859.
Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344087, A344088, A344089.
Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.

Programs

  • Mathematica
    Table[Reverse/@Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,30}]

A335122 Irregular triangle whose reversed rows are all integer partitions in graded reverse-lexicographic order.

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 3, 2, 2, 1, 1, 2, 1, 1, 1, 1, 5, 1, 4, 2, 3, 1, 1, 3, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 1, 5, 2, 4, 1, 1, 4, 3, 3, 1, 2, 3, 1, 1, 1, 3, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 7, 1, 6, 2, 5, 1, 1, 5, 3, 4, 1, 2, 4
Offset: 0

Views

Author

Gus Wiseman, May 24 2020

Keywords

Comments

First differs from A036036 for partitions of 6.
First differs from A334442 for partitions of 6.
Also reversed partitions in reverse-colexicographic order.

Examples

			The sequence of all reversed partitions begins:
  ()         (1,1,3)        (7)              (8)
  (1)        (1,2,2)        (1,6)            (1,7)
  (2)        (1,1,1,2)      (2,5)            (2,6)
  (1,1)      (1,1,1,1,1)    (1,1,5)          (1,1,6)
  (3)        (6)            (3,4)            (3,5)
  (1,2)      (1,5)          (1,2,4)          (1,2,5)
  (1,1,1)    (2,4)          (1,1,1,4)        (1,1,1,5)
  (4)        (1,1,4)        (1,3,3)          (4,4)
  (1,3)      (3,3)          (2,2,3)          (1,3,4)
  (2,2)      (1,2,3)        (1,1,2,3)        (2,2,4)
  (1,1,2)    (1,1,1,3)      (1,1,1,1,3)      (1,1,2,4)
  (1,1,1,1)  (2,2,2)        (1,2,2,2)        (1,1,1,1,4)
  (5)        (1,1,2,2)      (1,1,1,2,2)      (2,3,3)
  (1,4)      (1,1,1,1,2)    (1,1,1,1,1,2)    (1,1,3,3)
  (2,3)      (1,1,1,1,1,1)  (1,1,1,1,1,1,1)  (1,2,2,3)
We have the following tetrangle of reversed partitions:
                             0
                            (1)
                          (2)(11)
                        (3)(12)(111)
                   (4)(13)(22)(112)(1111)
             (5)(14)(23)(113)(122)(1112)(11111)
  (6)(15)(24)(114)(33)(123)(1113)(222)(1122)(11112)(111111)

Links

Crossrefs

Row lengths are A000041.
The version for reversed partitions is A026792.
The version for colex instead of revlex is A026791.
The version for lex instead of revlex is A080576.
The non-reflected version is A080577.
The number of distinct parts is A115623.
Taking Heinz numbers gives A129129.
The version for compositions is A228351.
Partition lengths are A238966.
Partition maxima are A331581.
The length-sensitive version is A334442.
Lexicographically ordered partitions are A193073.
Partitions in colexicographic order are A211992.
Cf. A036036, A036037, A112798, A129129, A228531, A296774, A334301, A334302, A334435, A334436, A334438, A334439.

Programs

  • Mathematica
    revlexsort[f_,c_]:=OrderedQ[PadRight[{c,f}]];
Reverse/@Join@@Table[Sort[IntegerPartitions[n],revlexsort],{n,0,8}]

A335124 Minimum part of the n-th reversed integer partition in Abramowitz-Stegun order; a(0) = 0.

Original entry on oeis.org

0, 1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 5, 1, 2, 1, 1, 1, 1, 6, 1, 2, 3, 1, 1, 2, 1, 1, 1, 1, 7, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 2, 3, 4, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 9, 1, 2, 3, 4, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 0

Views

Author

Gus Wiseman, May 24 2020

Keywords

Comments

The ordering of reversed partitions is first by sum, then by length, and finally lexicographically. The version for non-reversed partitions is A335123.

Examples

			Triangle begins:
  0
  1
  2 1
  3 1 1
  4 1 2 1 1
  5 1 2 1 1 1 1
  6 1 2 3 1 1 2 1 1 1 1
  7 1 2 3 1 1 1 2 1 1 1 1 1 1 1
  8 1 2 3 4 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1

Links

Crossrefs

Row lengths are A000041.
Partition minima of A036036.
The length of the same partition is A036043.
The maximum of the same partition is A049085.
The number of distinct parts in the same partition is A103921.
The Heinz number of the same partition is A185974.
The version for non-reversed partitions is A335123.
Lexicographically ordered reversed partitions are A026791.
Partitions in (sum/length/colex) order are A036037.
Partitions in opposite Abramowitz-Stegun (sum/length/revlex) order are A334439.
Cf. A124734, A193073, A334301, A334302, A334433, A334435.

Programs

  • Mathematica
    Table[If[n==0,{0},Min/@Sort[Reverse/@IntegerPartitions[n]]],{n,0,8}]

Formula

a(n) = A055396(A185974(n)).

A344085 Triangle of squarefree numbers first grouped by greatest prime factor, then sorted by omega, then in increasing order, read by rows.

Original entry on oeis.org

1, 2, 3, 6, 5, 10, 15, 30, 7, 14, 21, 35, 42, 70, 105, 210, 11, 22, 33, 55, 77, 66, 110, 154, 165, 231, 385, 330, 462, 770, 1155, 2310, 13, 26, 39, 65, 91, 143, 78, 130, 182, 195, 273, 286, 429, 455, 715, 1001, 390, 546, 858, 910, 1365, 1430, 2002, 2145, 3003, 5005, 2730, 4290, 6006, 10010, 15015, 30030
Offset: 1

Views

Author

Gus Wiseman, May 11 2021

Keywords

Comments

Differs from A339195 in having 77 before 66.

Examples

			Triangle begins:
   1
   2
   3   6
   5  10  15  30
   7  14  21  35  42  70 105 210

Crossrefs

Row lengths are A000079.
Grouping by greatest prime factor only gives A339195.
Row sums are 1 and A339360.
Cf. A001221, A005117, A005183, A014466, A019565, A187769, A209862.
Partition/composition orderings: A026791, A026792, A026793, A036036, A036037, A048793, A066099, A080577, A112798, A118457, A124734, A162247, A193073, A211992, A228100, A228531, A246688, A272020, A299755, A296774, A304038, A319247, A329631, A334301, A334302, A334439, A334442, A335122, A344086, A344087, A344088, A344089.
Partition/composition applications: A001793, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124.

Programs

  • Mathematica
    nn=4;
GatherBy[SortBy[Select[Range[Times@@Prime/@Range[nn]],SquareFreeQ[#]&&PrimePi[FactorInteger[#][[-1,1]]]<=nn&],PrimeOmega],FactorInteger[#][[-1,1]]&]

A344090 Flattened tetrangle of strict integer partitions, sorted first by sum, then by length, then lexicographically.

Original entry on oeis.org

1, 2, 3, 2, 1, 4, 3, 1, 5, 3, 2, 4, 1, 6, 4, 2, 5, 1, 3, 2, 1, 7, 4, 3, 5, 2, 6, 1, 4, 2, 1, 8, 5, 3, 6, 2, 7, 1, 4, 3, 1, 5, 2, 1, 9, 5, 4, 6, 3, 7, 2, 8, 1, 4, 3, 2, 5, 3, 1, 6, 2, 1, 10, 6, 4, 7, 3, 8, 2, 9, 1, 5, 3, 2, 5, 4, 1, 6, 3, 1, 7, 2, 1, 4, 3, 2, 1
Offset: 0

Views

Author

Gus Wiseman, May 12 2021

Keywords

Comments

The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)
  3: (3)(21)
  4: (4)(31)
  5: (5)(32)(41)
  6: (6)(42)(51)(321)
  7: (7)(43)(52)(61)(421)
  8: (8)(53)(62)(71)(431)(521)
  9: (9)(54)(63)(72)(81)(432)(531)(621)

Links

Crossrefs

Starting with reversed partitions gives A026793.
The version for compositions is A124734.
Showing partitions as Heinz numbers gives A246867.
The non-strict version is A334301 (reversed: A036036).
Ignoring length gives A344086 (reversed: A246688).
Same as A344089 with partitions reversed.
The version for revlex instead of lex is A344092.
A026791 reads off lexicographically ordered reversed partitions.
A080577 reads off reverse-lexicographically ordered partitions.
A112798 reads off reversed partitions by Heinz number.
A296150 reads off partitions by Heinz number.
Cf. A036037, A036043, A103921, A185974, A193073, A211992, A296774, A334302, A334433, A334435, A334438, A334439, A334440, A334441, A334442, A344091.

Programs

  • Mathematica
    Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,10}]

A344087 Flattened tetrangle of strict integer partitions sorted first by sum, then colexicographically.

Original entry on oeis.org

1, 2, 2, 1, 3, 3, 1, 4, 4, 1, 3, 2, 5, 3, 2, 1, 5, 1, 4, 2, 6, 4, 2, 1, 6, 1, 5, 2, 4, 3, 7, 5, 2, 1, 4, 3, 1, 7, 1, 6, 2, 5, 3, 8, 6, 2, 1, 5, 3, 1, 8, 1, 4, 3, 2, 7, 2, 6, 3, 5, 4, 9, 4, 3, 2, 1, 7, 2, 1, 6, 3, 1, 5, 4, 1, 9, 1, 5, 3, 2, 8, 2, 7, 3, 6, 4, 10
Offset: 0

Views

Author

Gus Wiseman, May 11 2021

Keywords

Comments

The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)
  3: (21)(3)
  4: (31)(4)
  5: (41)(32)(5)
  6: (321)(51)(42)(6)
  7: (421)(61)(52)(43)(7)
  8: (521)(431)(71)(62)(53)(8)
  9: (621)(531)(81)(432)(72)(63)(54)(9)

Links

Crossrefs

Positions of first appearances are A015724.
Triangle sums are A066189.
Taking revlex instead of colex gives A118457.
The not necessarily strict version is A211992.
Taking lex instead of colex gives A344086.
A026793 gives reversed strict partitions in A-S order (sum/length/lex).
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
A344090 gives strict partitions in A-S order (sum/length/lex).
Cf. A005117, A014466, A209862.
Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080576, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A319247, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344088, A344089, A344091.
Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.

Programs

  • Mathematica
    colex[f_,c_]:=OrderedQ[PadRight[{Reverse[f],Reverse[c]}]];
Table[Sort[Select[IntegerPartitions[n],UnsameQ@@#&],colex],{n,0,10}]

A344088 Flattened tetrangle of reversed strict integer partitions sorted first by sum, then colexicographically.

Original entry on oeis.org

1, 2, 1, 2, 3, 1, 3, 4, 2, 3, 1, 4, 5, 1, 2, 3, 2, 4, 1, 5, 6, 1, 2, 4, 3, 4, 2, 5, 1, 6, 7, 1, 3, 4, 1, 2, 5, 3, 5, 2, 6, 1, 7, 8, 2, 3, 4, 1, 3, 5, 4, 5, 1, 2, 6, 3, 6, 2, 7, 1, 8, 9, 1, 2, 3, 4, 2, 3, 5, 1, 4, 5, 1, 3, 6, 4, 6, 1, 2, 7, 3, 7, 2, 8, 1, 9, 10
Offset: 0

Views

Author

Gus Wiseman, May 12 2021

Keywords

Comments

The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)
  3: (12)(3)
  4: (13)(4)
  5: (23)(14)(5)
  6: (123)(24)(15)(6)
  7: (124)(34)(25)(16)(7)
  8: (134)(125)(35)(26)(17)(8)
  9: (234)(135)(45)(126)(36)(27)(18)(9)

Links

Crossrefs

Positions of first appearances are A015724.
Triangle sums are A066189.
The non-strict version is A080576.
Taking lex instead of colex gives A246688 (non-reversed: A344086).
The non-reversed version is A344087.
Taking revlex instead of colex gives A344089 (non-reversed: A118457).
A026793 gives reversed strict partitions in A-S order (sum/length/lex).
A319247 sorts strict partitions by Heinz number.
A329631 sorts reversed strict partitions by Heinz number.
A344090 gives strict partitions in A-S order (sum/length/lex).
Cf. A005117, A014466, A209862.
Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344091.
Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.

Programs

  • Mathematica
    colex[f_,c_]:=OrderedQ[PadRight[{Reverse[f],Reverse[c]}]];
Table[Sort[Reverse/@Select[IntegerPartitions[n],UnsameQ@@#&],colex],{n,0,10}]

A344091 Flattened tetrangle of all finite multisets of positive integers sorted first by sum, then by length, then colexicographically.

Original entry on oeis.org

1, 2, 1, 1, 3, 1, 2, 1, 1, 1, 4, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 5, 2, 3, 1, 4, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 3, 3, 2, 4, 1, 5, 2, 2, 2, 1, 2, 3, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1
Offset: 0

Views

Author

Gus Wiseman, May 12 2021

Keywords

Comments

First differs from A334302 for partitions of 9.
The zeroth row contains only the empty partition.
A tetrangle is a sequence of finite triangles.

Examples

			Tetrangle begins:
  0: ()
  1: (1)
  2: (2)(11)
  3: (3)(12)(111)
  4: (4)(22)(13)(112)(1111)
  5: (5)(23)(14)(122)(113)(1112)(11111)
  6: (6)(33)(24)(15)(222)(123)(114)(1122)(1113)(11112)(111111)

Links

Crossrefs

The version for lex instead of colex is A036036.
Starting with reversed partitions gives A036037.
Ignoring length gives A211992 (reversed: A080576).
Same as A334301 with partitions reversed.
The version for revlex instead of colex is A334302.
The Heinz numbers of these partitions are A334433.
The strict case is A344089.
A026791 reads off lexicographically ordered reversed partitions.
A080577 reads off reverse-lexicographically ordered partitions.
A112798 reads off reversed partitions by Heinz number.
A193073 reads off lexicographically ordered partitions.
A296150 reads off partitions by Heinz number.
Cf. A000041, A026793, A124734, A185974, A228531, A246688, A296774, A334433, A334435, A334438, A334439, A334441, A334442, A344086, A344090.

Programs

  • Mathematica
    Table[Reverse/@Sort[IntegerPartitions[n]],{n,0,9}]
Previous Showing 21-30 of 33 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.