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 1-6 of 6 results.

A165762 Areas for which there are more tatami-free rooms (cf. A165633) than for any smaller size.

Original entry on oeis.org

70, 198, 336, 504, 1320, 1440, 3360, 5040, 6720, 10080, 15120, 30240, 45360, 55440, 110880, 166320, 221760, 327600, 360360, 415800, 554400, 720720, 1081080, 1441440, 2162160, 2494800, 2882880
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

A165761 Indices of records in A165633.

Original entry on oeis.org

1, 14, 36, 68, 237, 263, 709, 1111, 1520, 2350, 3605, 7437, 11325, 13921, 28337, 42896, 57483, 85499, 94206, 108922, 145872, 190311, 286903, 383819, 578215, 668153, 773158
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

Comments

A165632(a(n))=A165762(n) are areas for which there are more

Links

A165763 Records in A165633.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 18, 21, 22, 27, 33, 35, 39, 40, 43, 46, 51, 59, 63, 70, 74, 76
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

Comments

A165632(A165761(n))=A165762(n) are areas for which there are more tatami-free rooms than for any smaller size, this sequence gives that number of tatami-free rooms.

Links

Formula

A165763(n)=A165633(A165761(n))

A165765 Index of first occurrence of n in A165633.

Original entry on oeis.org

1, 14, 36, 68, 237, 263, 790, 709, 1111, 1931, 1520, 2350, 3981, 4028, 4450, 4875, 3605, 8208, 9373, 7437, 11325, 18708, 15225, 16525, 21777, 13921, 31975, 36641, 35608, 38913, 33628, 46533, 66817, 28337, 42896, 76805, 64813, 57483, 100212
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

Examples

			a(7)>a(8) since the minimal size for which there are exactly 7 tatami free rooms is larger than the minimal size for which there are exactly 8 tatami free rooms.

Formula

A165764(n) = min { k | A165633(k)=n }

A165632 Sizes of tatami-free rooms.

Original entry on oeis.org

70, 88, 96, 108, 126, 130, 140, 150, 154, 160, 176, 180, 192, 198, 204, 208, 216, 228, 234, 238, 240, 250, 252, 260, 266, 270, 280, 286, 294, 300, 304, 308, 320, 322, 330, 336, 340, 348, 352, 360, 368, 372, 374, 378, 384, 390, 396, 400, 408, 414, 416, 418
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

Comments

Even numbers s such that some rectangle of size s=r*c (r,c positive integers) cannot be tiled with tatamis of size 1x2 such that not more than 3 tatamis meet at any point.
The number of different rectangles of size a(n) which have this property is given in A165633(n).

Examples

			a(1)=70 because the rectangle of size 7x10 is the smallest that cannot be filled with 2x1 tiles without having 4 tiles meet in some point.

Links

Crossrefs

Cf. A068920.

Formula

A165632 = { r*c in 2Z | A068920(r,c)=0 }

A165764 Smallest size of which there are n tatami-free rooms.

Original entry on oeis.org

70, 198, 336, 504, 1320, 1440, 3696, 3360, 5040, 8400, 6720, 10080, 16632, 16800, 18480, 20160, 15120, 33264, 37800, 30240, 45360, 73920, 60480, 65520, 85680, 55440, 124740, 142560, 138600, 151200, 131040, 180180, 257040, 110880, 166320
Offset: 1

Views

Author

M. F. Hasler, Sep 26 2009

Keywords

Comments

A tatami-free room is a rectangle of even size that allows no 1x2 domino tiling satisfying the tatami rule, i.e. such that there is no point in which 4 tiles meet.
a(n)=A165632(A165765(n)) where A165765(n) is the least index for which A165633(A165765(n))=n.

Examples

			The smallest tatami-free room is of size 7x10, and all other rectangles of this size allow for a tatami tiling, thus a(1) = 70.
a(5)=1320 is the smallest size of which there are exactly 5 tatami-free rooms, namely 20x66, 22x60, 24x55, 30x44 and 33x40.

Links

Formula

A165764(n) = A165632(A165765(n)) = min { r*c in 2Z | #{{r,c} | A068920(r,c)=0 } = n }
Showing 1-6 of 6 results.

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