A029826 -id:A029826 - cp's OEIS frontend

A225393 Expansion of 1/(1 - x - x^2 + x^6 - x^8).

1, 1, 2, 3, 5, 8, 12, 19, 30, 47, 74, 116, 183, 288, 453, 713, 1122, 1766, 2779, 4373, 6882, 10830, 17043, 26820, 42206, 66419, 104522, 164484, 258845, 407339, 641021, 1008761, 1587466, 2498162, 3931305, 6186612, 9735741, 15320931, 24110227, 37941757, 59708145

Offset: 0

Roger L. Bagula, May 06 2013

G. C. Greubel, Table of n, a(n) for n = 0..1000
Mohammed L. Nadji, Moussa Ahmia, Daniel F. Checa, and José L. Ramírez, Arndt Compositions with Restricted Parts, Palindromes, and Colored Variants, J. Int. Seq. (2025) Vol. 28, Issue 3, Article 25.3.6. See p. 8.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,-1,0,1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^2+x^6-x^8))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x - x^2 + x^6 - x^8), {x, 0, 50}], x]
LinearRecurrence[{1,1,0,0,0,-1,0,1},{1,1,2,3,5,8,12,19},50] (* G. C. Greubel, Nov 16 2016 *)

Vec(1/(1-x-x^2+x^6-x^8) + O(x^50)) \\ G. C. Greubel, Nov 16 2016

G.f.: 1/(1 - x - x^2 + x^6 - x^8).

a(n) = a(n-1) + a(n-2) - a(n-6) + a(n-8). - Ilya Gutkovskiy, Nov 16 2016

A225394 Expansion of 1/(1 - x - x^2 + x^7 - x^9).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 20, 32, 51, 81, 129, 205, 326, 519, 826, 1314, 2091, 3327, 5294, 8424, 13404, 21328, 33937, 54000, 85924, 136721, 217548, 346159, 550803, 876429, 1394560, 2219002, 3530841, 5618219, 8939622, 14224586, 22633938, 36014767, 57306132, 91184618

Offset: 0

Roger L. Bagula, May 06 2013

Limiting ratio is 1.59118..., the largest real root of -1 + x^2 - x^7 - x^8 + x^9 = 0.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,0,-1,0,1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^2+x^7-x^9))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x - x^2 + x^7 - x^9), {x, 0, 50}], x]
LinearRecurrence[{1,1,0,0,0,0,-1,0,1}, {1,1,2,3,5,8,13,20,32}, 50] (* G. C. Greubel, Nov 16 2016 *)

Vec(1/(1-x-x^2+x^7-x^9) + O(x^50)) \\ G. C. Greubel, Nov 16 2016

a(n) = a(n-1) + a(n-2) - a(n-7) + a(n-9). - Ilya Gutkovskiy, Nov 16 2016

A225499 Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).

Original entry on oeis.org

1, 1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 9, 11, 13, 16, 20, 25, 31, 39, 48, 59, 74, 92, 113, 140, 175, 217, 269, 334, 414, 513, 637, 791, 981, 1217, 1510, 1874, 2325, 2884, 3578, 4440, 5509, 6835, 8481, 10522, 13054, 16197, 20097, 24934, 30936, 38384

Offset: 0

Roger L. Bagula, May 09 2013

Limiting ratio is 1.24073..., the largest real root of 1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12: 1.240726423652541392056148161575

is a candidate for the smallest degree-12 Salem number.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,0,0,1,0,0,1,-1,1,-1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12), {x, 0, 50}], x]
LinearRecurrence[{1,-1,1,0,0,1,0,0,1,-1,1,-1},{1,1,0,0,1,1,1,2,2,2,3,4},100] (* G. C. Greubel, Nov 16 2016 *)

Vec(1/(1 -x +x^2 -x^3 -x^6 -x^9 +x^10 -x^11 +x^12) + O(x^50)) \\ G. C. Greubel, Nov 16 2016

a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-6) + a(n-9) - a(n-10) + a(n-11) - a(n-12). - Franck Maminirina Ramaharo, Nov 02 2018

A143438 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6), with a(0) = a(2) = a(3) = 1, a(1) = 0 and a(4) = a(5) = 2.

Original entry on oeis.org

1, 0, 1, 1, 2, 2, 3, 5, 6, 9, 12, 18, 24, 34, 48, 67, 94, 131, 185, 258, 362, 507, 711, 996, 1395, 1956, 2740, 3840, 5380, 7540, 10565, 14804, 20745, 29069, 40734, 57078, 79983, 112077, 157050, 220069, 308376, 432118, 605512, 848486, 1188956, 1666047, 2334578

Offset: 0

Roger L. Bagula and Gary W. Adamson, Oct 23 2008

Expansion of 1/p(x), where p(x) = 1 - x^2 - x^3 - x^4 + x^6 is a Salem polynomial.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Curtis T. McMullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, 2001.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,0,-1).

Cf. A029826, A117791, A143419, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

a:=[1,0,1,1,2,2];; for n in [7..50] do a[n]:=a[n-2]+a[n-3]+a[n-4]-a[n-6]; od; a; # G. C. Greubel, Dec 06 2019

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^2-x^3-x^4+x^6))); // G. C. Greubel, Nov 03 2018

seq(coeff(series(1/(1-x^2-x^3-x^4+x^6), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 06 2019

CoefficientList[Series[1/(1-x^2-x^3-x^4+x^6), {x, 0, 50}], x]
LinearRecurrence[{0,1,1,1,0,-1}, {1,0,1,1,2,2}, 50] (* G. C. Greubel, Dec 06 2019 *)

makelist(ratcoef(taylor(1/(1 -x^2 -x^3 -x^4 +x^6), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Oct 31 2018 */

my(x='x+O('x^50)); Vec(1/(1-x^2-x^3-x^4+x^6)) \\ G. C. Greubel, Nov 03 2018

def A143438_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(1/(1-x^2-x^3-x^4+x^6)).list()
A143438_list(50) # G. C. Greubel, Dec 06 2019

G.f.: 1/(1 - x^2 - x^3 - x^4 + x^6). - Colin Barker, Nov 24 2012

Edited, new name (after Colin Barker), more terms, and offset corrected by Franck Maminirina Ramaharo, Oct 30 2018

A143472 Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.

Original entry on oeis.org

1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 20, 26, 31, 38, 48, 58, 72, 88, 108, 134, 164, 202, 249, 306, 376, 463, 570, 701, 863, 1061, 1306, 1607, 1976, 2433, 2993, 3682, 4531, 5574, 6859, 8439, 10383, 12776, 15719, 19340, 23796

Offset: 0

Roger L. Bagula and Gary W. Adamson, Oct 24 2008

The ratio productive positive root is 1.2303914344072246.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1,0,1,0,0,-1).

Cf. A029826, A117791, A143419, A143438, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^5-x^7+x^10))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x^3 - x^5 - x^7 + x^10), {x, 0, 50}], x]

makelist(ratcoef(taylor(1/(1 - x^3 - x^5 - x^7 + x^10), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Nov 02 2018 */

x='x+O('x^50); Vec(1/(1-x^3-x^5-x^7+x^10)) \\ G. C. Greubel, Nov 03 2018

G.f.: 1/(1 - x^3 - x^5 - x^7 + x^10). - Colin Barker, Oct 23 2013

a(n) = a(n-3) + a(n-5) + a(n-7) - a(n-10). - Franck Maminirina Ramaharo, Oct 30 2018

More terms from Colin Barker, Oct 23 2013

New name after Colin Barker's formula by Franck Maminirina Ramaharo, Nov 03 2018

A143619 Expansion of 1/(1 - x^2 - x^7 - x^12 + x^14) (a Salem polynomial).

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 8, 9, 12, 13, 17, 19, 24, 28, 34, 41, 49, 59, 71, 86, 103, 124, 149, 179, 215, 259, 311, 375, 450, 542, 651, 784, 942, 1133, 1363, 1638, 1971, 2369, 2851, 3427, 4123, 4957, 5962, 7170, 8622, 10370, 12470, 14998, 18035, 21691, 26085, 31371

Offset: 0

Roger L. Bagula and Gary W. Adamson, Oct 26 2008

Low growth rate of 1.20262... .The absolute values of the roots of the polynomial are 0.8315201041..., 1.2026167436..., and 1.0 (with multiplicity 12). The polynomial is self-reciprocal. - Joerg Arndt, Nov 03 2012

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,1,0,0,0,0,1,0,-1).

Cf. A029826, A117791, A143419, A143438, A143472, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x^2-x^7-x^12+x^14))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x^2 - x^7 - x^12 + x^14), {x, 0, 50}], x]
LinearRecurrence[{0,1,0,0,0,0,1,0,0,0,0,1,0,-1},{1,0,1,0,1,0,1,1,1,2,1,3,2,4},70] (* Harvey P. Dale, Aug 08 2022 *)

x='x+O('x^50); Vec(1/(1-x^2-x^7-x^12+x^14)) \\ G. C. Greubel, Nov 03 2018

G.f.: 1/(1 - x^2 - x^7 - x^12 + x^14). - Colin Barker, Nov 03 2012

a(n) = a(n-2) + a(n-7) + a(n-12) - a(n-14). - Franck Maminirina Ramaharo, Nov 02 2018

New name from Colin Barker and Joerg Arndt, Nov 03 2012

A143644 Expansion of 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14) (a Salem polynomial).

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5, 6, 7, 9, 10, 12, 15, 18, 21, 26, 31, 37, 44, 54, 64, 76, 92, 111, 132, 159, 191, 229, 275, 330, 396, 475, 570, 684, 821, 985, 1182, 1418, 1703, 2043, 2451, 2942, 3531, 4236, 5084, 6101, 7321, 8785, 10543, 12652, 15182, 18219, 21864, 26237, 31485

Offset: 0

Roger L. Bagula and Gary W. Adamson, Oct 26 2008

Limiting ratio is 1.2000265239873915..., the largest real root of 1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14: 1.200026523987391518902962100414 is a candidate for the smallest degree-14 Salem number. The absolute values of the roots of the polynomial are 0.8333149143..., 1.200026523..., and 1.0 (with multiplicity 12). The polynomial is self-reciprocal. - Joerg Arndt, Nov 03 2012

G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,0,-1,0,0,1,1,0,0,-1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) )); // G. C. Greubel, Dec 06 2019

seq(coeff(series(1/(1-x^3-x^4+x^7-x^10-x^11+x^14), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 06 2019

CoefficientList[Series[1/(1-x^3-x^4+x^7-x^10-x^11+x^14), {x, 0, 50}], x]

my(x='x+O('x^50)); Vec(1/(1-x^3-x^4+x^7-x^10-x^11+x^14)) \\ G. C. Greubel, Dec 06 2019

def A143644_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^3-x^4+x^7-x^10-x^11+x^14) ).list()
A143644_list(50) # G. C. Greubel, Dec 06 2019

G.f.: 1/(1 - x^3 - x^4 + x^7 - x^10 - x^11 + x^14). - Colin Barker, Nov 03 2012

a(n) = a(n-3) + a(n-4) - a(n-7) + a(n-10) + a(n-11) - a(n-14). - Franck Maminirina Ramaharo, Oct 30 2018

New name from Colin Barker and Joerg Arndt, Nov 03 2012

A147663 Expansion of 1/(1 - x - x^2 + x^3 - x^7 + x^9 - x^11).

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 50, 66, 88, 116, 154, 203, 269, 356, 472, 625, 828, 1097, 1453, 1925, 2550, 3379, 4476, 5930, 7855, 10406, 13784, 18260, 24189, 32044, 42449, 56233, 74493, 98682, 130726, 173175, 229409, 303902, 402585

Offset: 0

Roger L. Bagula, Nov 09 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Curtis T. McMullen, Dynamics on K3 surfaces: Salem numbers and Siegel disks, 2005.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,1,0,-1,0,1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1 -x-x^2+x^3-x^7+x^9-x^11))); // G. C. Greubel, Nov 03 2018

CoefficientList[Series[1/(1 - x - x^2 + x^3 - x^7 + x^9 - x^11), {x, 0, 50}], x] (* Franck Maminirina Ramaharo, Oct 31 2018 *)
LinearRecurrence[{1,1,-1,0,0,0,1,0,-1,0,1},{1,1,2,2,3,3,4,5,7,9,12},50] (* Harvey P. Dale, May 31 2020 *)

Vec(-1/((x^3+x^2-1)*(x^8-x^7+x^5-x^4+x^3-x+1))  + O(x^50)) \\ Colin Barker, Sep 18 2013

G.f.: -1/((x^3 + x^2 - 1)*(x^8 - x^7 + x^5 - x^4 + x^3 - x + 1)). - Colin Barker, Sep 18 2013

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-7) - a(n-9) + a(n-10), n >= 10. - Franck Maminirina Ramaharo, Oct 31 2018

Heavily edited (because the Name, Comments, Formula and Mathematica code did not correspond to the terms of the sequence) by Colin Barker, Sep 18 2013

A173908 Expansion of 1/(1 + x - x^3 - x^4 - x^8 - x^12 - x^13 - x^17 - x^21 - x^22 - x^26 - x^30 - x^31 + x^33 + x^34).

Original entry on oeis.org

1, -1, 1, 0, 0, 0, 1, -1, 2, -2, 3, -2, 3, -2, 4, -3, 6, -5, 9, -7, 12, -9, 16, -12, 22, -17, 31, -24, 43, -33, 59, -45, 81, -63, 113, -88, 156, -121, 215, -168, 298, -233, 412, -323, 570, -448, 788, -621, 1090, -861, 1507, -1193, 2084, -1654, 2882, -2293

Offset: 0

Roger L. Bagula, Nov 26 2010

This polynomial is what I call a bi-Salem polynomial because it has two roots bigger than 1 (one positive and one negative).

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,0,0,1,0,0,0,1,1,0,-1,-1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

m:=60; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1+x-x^3 -x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+x^33+x^34))); // G. C. Greubel, Nov 03 2018

seq(coeff(series(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30-x^31+ x^33+x^34), x, n+1), x, n), n = 0..60); # G. C. Greubel, Dec 15 2019

CoefficientList[Series[1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34), {x, 0, 60}], x]

x='x+O('x^60); Vec(1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26 - x^30-x^31+x^33+x^34)) \\ G. C. Greubel, Nov 03 2018

def A173908_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1+x-x^3-x^4-x^8-x^12-x^13-x^17-x^21-x^22-x^26-x^30 - x^31+x^33+x^34) ).list()
A173908_list(30) # G. C. Greubel, Dec 15 2019

a(n) = a(n-1) + (n-3) + a(n-4) + a(n-8) + a(n-12) + a(n-13) + a(n-17) + a(n-21) + a(n-22) + a(n-26) + a(n-30) + a(n-31) - a(n-33) - a(n-34). - Franck Maminirina Ramaharo, Nov 02 2018

A173924 Expansion of 1/(1 - x^5 - x^6 - x^7 - x^8 + x^13).

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 3, 3, 3, 3, 4, 6, 8, 10, 11, 12, 16, 20, 26, 32, 38, 46, 56, 70, 88, 108, 132, 161, 198, 244, 302, 372, 457, 561, 689, 849, 1046, 1287, 1584, 1947, 2395, 2947, 3627, 4464, 5492, 6756, 8312, 10227, 12584, 15484, 19052, 23440

Offset: 0

Roger L. Bagula, Nov 26 2010

Limiting ratio is: 1.2303914344072246.
Related to the 7th Salem on the Mossinghoff's list by factorization:
(1 + x)*(1 - x + x^2)*(1 - x^3 - x^5 - x^7 + x^10)

G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Mossinghoff, Small Salem Numbers
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,1,1,1,0,0,0,0,-1).

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225391, A225393, A225394, A225482, A225499.

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!(1/(1 -x^5-x^6-x^7-x^8+x^13))); // G. C. Greubel, Nov 03 2018

seq(coeff(series(1/(1-x^5-x^6-x^7-x^8+x^13), x, n+1), x, n), n = 0..50); # G. C. Greubel, Dec 15 2019

CoefficientList[Series[1/(1-x^5-x^6-x^7-x^8+x^13), {x, 0, 50}], x]

my(x='x+O('x^50)); Vec(1/(1-x^5-x^6-x^7-x^8+x^13)) \\ G. C. Greubel, Nov 03 2018

def A173924_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x^5-x^6-x^7-x^8+x^13) ).list()
A173924_list(50) # G. C. Greubel, Dec 15 2019

a(n) = a(n-5) + a(n-6) + a(n-7) + a(n-8) - a(n-13). - Franck Maminirina Ramaharo, Oct 30 2018

More terms from Franck Maminirina Ramaharo, Nov 03 2018

cp's OEIS Frontend

A225393 Expansion of 1/(1 - x - x^2 + x^6 - x^8).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A225394 Expansion of 1/(1 - x - x^2 + x^7 - x^9).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A225499 Expansion of 1/(1 - x + x^2 - x^3 - x^6 - x^9 + x^10 - x^11 + x^12).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A143438 a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6), with a(0) = a(2) = a(3) = 1, a(1) = 0 and a(4) = a(5) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

Maxima

PARI

Sage

Formula

Extensions

A143472 Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Formula

Extensions

A143619 Expansion of 1/(1 - x^2 - x^7 - x^12 + x^14) (a Salem polynomial).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions