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.

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A056432 Step cyclic shifted sequence structures using a maximum of five different symbols.

Original entry on oeis.org

1, 2, 3, 7, 8, 36, 35, 201, 393, 2370, 3971, 46094, 66675, 613439, 2139350, 10016839, 23424253, 294723254, 465082931, 4972761822, 15773188813, 90323063945, 196342666487, 2587522663248, 4967200045397, 39800811900389
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. Permuting the symbols will not change the structure.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056413.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.

A056395 Number of step shifted (decimated) sequence structures using a maximum of six different symbols.

Original entry on oeis.org

1, 2, 4, 11, 18, 117, 161, 1193, 3530, 27569, 60333, 863409, 1636609, 19122031, 84580125, 501915567, 1492170609, 23751685183, 47340359591, 637742820401, 2546703019245, 18317620839483, 49923584451715
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts. Permuting the symbols will not change the structure.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056375.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.

A056433 Step cyclic shifted sequence structures using a maximum of six different symbols.

Original entry on oeis.org

1, 2, 3, 7, 8, 37, 36, 219, 452, 3000, 5652, 74961, 126758, 1371016, 5653854, 31440841, 87796362, 1319722484, 2491714134, 31893717065, 121274777228, 832622962686, 2170594048582, 34308978981089
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. Permuting the symbols will not change the structure.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056414.

Formula

Use de Bruijn's generalization of Polya's enumeration theorem as discussed in reference.

A056442 Number of primitive (period n) step cyclic shifted sequence structures using a maximum of five different symbols.

Original entry on oeis.org

1, 1, 2, 5, 7, 32, 34, 194, 390, 2361, 3970, 46053, 66674, 613403, 2139340, 10016638, 23424252, 294722828, 465082930, 4972759447, 15773188776, 90323059973, 196342666486, 2587522616960, 4967200045389, 39800811833713
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts. Under step cyclic shifts, abcde, bdace, bcdea, cdeab and daceb etc. are equivalent. Permuting the symbols will not change the structure.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056422.

Formula

sum mu(d)*A056432(n/d) where d|n.

A063379 Number of orbits of the group of units of Z/(n) acting naturally on the 2-subsets of Z/(n).

Original entry on oeis.org

1, 2, 4, 3, 9, 4, 11, 8, 13, 6, 25, 7, 17, 18, 24, 9, 33, 10, 35, 23, 25, 12, 59, 18, 29, 26, 45, 15, 71, 16, 49, 33, 37, 32, 86, 19, 41, 38, 81, 21, 91, 22, 65, 61, 49, 24, 123, 32, 73, 48, 75, 27, 105, 46, 103, 53, 61, 30, 181, 31, 65, 78, 98, 53, 131, 34
Offset: 2

Views

Author

W. Edwin Clark, Jul 15 2001

Keywords

Examples

			a(3) = 2 since when U(3) = {1,2} acts naturally on the three 2-subsets {0,1}, {0,2}, {1,2} of Z/(3) the orbits are {{0,1},{0,2}} and {{1,2}}. Note that 2{0,1} = {0,2} but there is no unit a in U(3) such that a{0,1} = {1,2}.

Crossrefs

Cf. A065957, A063381, A000005, A056376 + 1, A056371 - 1

Extensions

More terms from Sean A. Irvine, Apr 22 2023

A056377 Number of step shifted (decimated) sequences using exactly three different symbols.

Original entry on oeis.org

0, 0, 3, 21, 39, 288, 309, 1659, 3102, 14148, 17157, 136227, 130995, 790128, 1791489, 5427597, 8047839, 64467180, 64486017, 437324331, 871627041, 3136899816, 4278115101, 35355632943, 42359479638
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056372.

Formula

A056372(n)-3*A056371(n)+3.

A056378 Number of step shifted (decimated) sequences using exactly four different symbols.

Original entry on oeis.org

0, 0, 0, 12, 60, 792, 1404, 10716, 31200, 205032, 349956, 3727932, 5065804, 41574312, 127199028, 517290132, 1041517620, 11195637720, 15012935676, 135825699612, 363040469732, 1746670165416, 3181465294092
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056373.

Formula

A056373(n)-4*A056372(n)+6*A056371(n)-4.

A056379 Number of step shifted (decimated) sequences using exactly five different symbols.

Original entry on oeis.org

0, 0, 0, 0, 30, 900, 2800, 32010, 139080, 1276200, 2960940, 41626230, 75086430, 801522300, 3162262170, 16463793480, 42395689530, 579164463000, 983928850100, 11241277288950, 37913042835300
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056374.

Formula

A056374(n)-5*A056373(n)+10*A056372(n)-10*A056371(n)+5.

A056380 Number of step shifted (decimated) sequences using exactly six different symbols.

Original entry on oeis.org

0, 0, 0, 0, 0, 360, 2520, 48060, 317520, 4109040, 12923136, 238785300, 559279980, 7612396920, 37864711260, 246263046840, 787758864480, 13282478342640, 27723264985920, 387585098313300, 1595144664456720
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056375.

Formula

A056375(n)-6*A056374(n)+15*A056373(n)-20*A056372(n)+15*A056371(n)-6.

A056401 Number of primitive (aperiodic) step shifted (decimated) sequence structures using a maximum of two different symbols.

Original entry on oeis.org

1, 1, 2, 4, 5, 16, 13, 42, 49, 133, 107, 600, 351, 1385, 2164, 4416, 4115, 22043, 14601, 67872, 88360, 209827, 190745, 1074534, 839122, 2796647, 3730532, 11275300, 9587579, 67193198, 35792567
Offset: 1

Views

Author

Marks R. Nester

Keywords

Comments

See A056371 for an explanation of step shifts. Permuting the symbols will not change the structure.

References

  • M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Cf. A056381.

Formula

Sum mu(d)*A056391(n/d) where d divides n.
Previous Showing 21-30 of 86 results. Next

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