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 1-10 of 12 results. Next

A054660 Number of monic irreducible polynomials over GF(4) of degree n with fixed nonzero trace.

Original entry on oeis.org

1, 2, 5, 16, 51, 170, 585, 2048, 7280, 26214, 95325, 349520, 1290555, 4793490, 17895679, 67108864, 252645135, 954437120, 3616814565, 13743895344, 52357696365, 199911205050, 764877654105, 2932031006720, 11258999068416
Offset: 1

Views

Author

N. J. A. Sloane, Apr 18 2000

Keywords

Comments

Also number of Lyndon words of length n with trace 1 over GF(4).
Let x = RootOf( z^2+z+1 ) and y = 1+x. Also number of Lyndon words of length n with trace x over GF(4). Also number of Lyndon words of length n with trace y over GF(4).
Also number of 4-ary Lyndon words (i.e., Lyndon words over Z_4) of length n with trace 1 (mod 4). Also the same with trace 3 (mod 4). - Andrey Zabolotskiy, Dec 19 2020

Examples

			a(3; y)=5 since the five Lyndon words over GF(4) of trace y and length 3 are { 00y, 01x, 0x1, 11y, xxy }; the five Lyndon words over Z_4 of trace 1 (mod 4) and length 3 are { 001, 023, 032, 113, 122 }.

Links

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054661, etc.
Cf. A008683, A054661, A027377, A300628, A074033, A074034, A074035, A074448, A074449, A074450.
Cf. A074406, A074407, A074408, A074409.

Formula

From Seiichi Manyama, Mar 11 2018: (Start)
a(n) = A000048(2*n) = (1/(4*n)) * Sum_{odd d divides n} mu(d)*4^(n/d), where mu is the Möbius function A008683.
a(n+1) = A300628(n,n) for n >= 0. (End)
From Andrey Zabolotskiy, Dec 19 2020: (Start)
a(n) = A074033(n) + A074034(n) + 2 * A074035(n).
a(n) = A074448(n) + A074449(n) + 2 * A074450(n).
a(n) = A074406(n) + A074407(n) + A074408(n) + A074409(n). (End)

Extensions

More terms from James Sellers, Apr 19 2000

A074411 Number of 4-ary Lyndon words of length n over Z_4 with trace 2 and subtrace 1.

Original entry on oeis.org

0, 0, 2, 4, 16, 36, 128, 440, 1706, 6560, 24576, 90046, 327680, 1197824, 4438966, 16645120, 62914560, 238609052, 905969664, 3442670796, 13102206738, 49977704448, 191126044672, 732649663000, 2814062572336, 10825960652800, 41705086880768, 160862475611574
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074407, A074408, A074409, A074410, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A068596 Number of 4-ary Lyndon words whose trace and subtrace are both 0 mod 4.

Original entry on oeis.org

1, 0, 1, 1, 11, 44, 169, 588, 1948, 6560, 23133, 84565, 317755, 1198336, 4509419, 16909184, 63409935, 238609052, 902444517, 3429249843, 13076666409, 49977802752, 191312873561, 733365845820, 2815437297416, 10825960652800, 41694907460224, 160823207301705
Offset: 1

Views

Author

Frank Ruskey, Mar 28 2002

Keywords

Comments

The trace of a word is the sum of its characters; the subtrace of a word is the sum of all products of pairs of its characters.

Links

Crossrefs

Cf. A074403, A074404, A074405, A074406, A074407, A074408, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074403 Number of 4-ary Lyndon words of length n over Z_4 with trace 0 and subtrace 1.

Original entry on oeis.org

0, 0, 2, 6, 16, 45, 128, 448, 1706, 6528, 24576, 90110, 327680, 1198665, 4438966, 16646144, 62914560, 238605640, 905969664, 3442684722, 13102206738, 49977848925, 191126044672, 732649837760, 2814062572336, 10825959997440, 41705086880768, 160862477970870
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Links

Crossrefs

Cf. A068596, A074404, A074405, A074406, A074407, A074408, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074404 Number of 4-ary Lyndon words of length n over Z_4 with trace 0 and subtrace 2.

Original entry on oeis.org

0, 0, 0, 1, 8, 36, 160, 548, 1920, 6496, 23040, 84565, 317440, 1197824, 4508328, 16905344, 63406080, 238602228, 902430720, 3429249843, 13076616480, 49977704448, 191312691200, 733365135860, 2815436626328, 10825959342080, 41694904974720, 160823207301705
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Links

Crossrefs

Cf. A068596, A074403, A074405, A074406, A074407, A074408, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074405 Number of 4-ary Lyndon words of length n over Z_4 with trace 0 and subtrace 3.

Original entry on oeis.org

0, 1, 2, 6, 16, 40, 128, 448, 1706, 6579, 24576, 90110, 327680, 1198080, 4438966, 16646144, 62914560, 238612920, 905969664, 3442684722, 13102206738, 49977753600, 191126044672, 732649837760, 2814062572336, 10825961287995, 41705086880768, 160862477970870
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Links

Crossrefs

Cf. A068596, A074403, A074404, A074406, A074407, A074408, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074407 Number of 4-ary Lyndon words of length n over Z_4 with trace 1 and subtrace 1.

Original entry on oeis.org

0, 0, 0, 4, 16, 53, 169, 512, 1706, 6144, 23040, 87380, 327680, 1217097, 4509419, 16777216, 62914560, 237677216, 902430720, 3435973836, 13102206738, 50026607709, 191312873561, 733007751680, 2814062572336, 10823317585920, 41694904974720, 160842843834660
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Comments

Same as the number of 4-ary Lyndon words of length n over Z_4 with trace 3 and subtrace 1.

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074408, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074408 Number of 4-ary Lyndon words of length n over Z_4 with trace 1 and subtrace 2.

Original entry on oeis.org

0, 1, 2, 4, 11, 32, 128, 512, 1920, 6963, 24576, 87380, 317755, 1179648, 4438966, 16777216, 63406080, 239541344, 905969664, 3435973836, 13076666409, 49928994816, 191126044672, 733007751680, 2815436626328, 10828603699515, 41705086880768, 160842843834660
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Comments

Same as the number of 4-ary Lyndon words of length n over Z_4 with trace 3 and subtrace 2.

Examples

			a(3;1,2)=2 since the two 4-ary Lyndon words of trace 1, subtrace 2 and length 3 are { 023, 032 }.

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074407, A074409, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074409 Number of 4-ary Lyndon words of length n over Z_4 with trace 1 and subtrace 3.

Original entry on oeis.org

0, 0, 1, 4, 16, 53, 160, 512, 1706, 6144, 23133, 87380, 327680, 1217097, 4508328, 16777216, 62914560, 237677216, 902444517, 3435973836, 13102206738, 50026607709, 191312691200, 733007751680, 2814062572336, 10823317585920, 41694907460224, 160842843834660
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Comments

Same as the number of 4-ary Lyndon words of length n over Z_4 with trace 3 and subtrace 3.

Examples

			a(4;3,3)=4 since the four 4-ary Lyndon words of trace 3, subtrace 3 and length 4 are { 0111, 0133, 0313, 0331 }.

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074407, A074408, A074410, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013

A074410 Number of 4-ary Lyndon words of length n over Z_4 with trace 2 and subtrace 0.

Original entry on oeis.org

1, 1, 1, 4, 11, 45, 169, 576, 1948, 6579, 23133, 84820, 317755, 1198665, 4509419, 16908288, 63409935, 238612920, 902444517, 3429289164, 13076666409, 49977848925, 191312873561, 733365665600, 2815437297416, 10825961287995, 41694907460224, 160823214491940
Offset: 1

Views

Author

Frank Ruskey and Nate Kube, Aug 22 2002

Keywords

Links

Crossrefs

Cf. A068596, A074403, A074404, A074405, A074406, A074407, A074408, A074409, A074411, A074412, A074413.

Extensions

Terms a(15) onward from Max Alekseyev, Apr 09 2013
Showing 1-10 of 12 results. Next

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

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