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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A124707 Number of base 14 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 14, 40, 92, 244, 644, 1750, 4802, 13324, 37244, 104770, 296222, 841114, 2396954, 6851920, 19639652, 56426044, 162453884, 468581890, 1353822062, 3917298334, 11350084334, 32926503100, 95626832432, 278010277474, 809008239794, 2356265478100, 6868253600552
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n) = a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 14) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,14}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

Crossrefs

Except for the first term, row 14 of A276562.
Cf. A002426, A124696.

Formula

G.f.: -(120*x^13 -55*x^12 -1200*x^11 +900*x^10 +2864*x^9 -3087*x^8 -1584*x^7 +3135*x^6 -792*x^5 -627*x^4 +416*x^3 -78*x^2 +1) / ((2*x-1) *(x^2-3*x+1) *(x^2+x-1) *(x^4+3*x^3-x^2-3*x+1) *(5*x^4-5*x^3-5*x^2+5*x-1)). - Alois P. Heinz, Apr 02 2025

A124708 Number of base 15 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 15, 43, 99, 263, 695, 1891, 5195, 14431, 40383, 113723, 321875, 914903, 2609895, 7468147, 21427259, 61622671, 177588815, 512734699, 1482818915, 4294677703, 12455435063, 36167638627, 105140060555, 305958613855, 891185076095
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 15) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,15}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124709 Number of base 16 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 16, 46, 106, 282, 746, 2032, 5588, 15538, 43522, 122676, 347528, 988692, 2822836, 8084374, 23214866, 66819298, 192723746, 556887508, 1611815768, 4672057072, 13560785792, 39408774154, 114653288678, 333906950236
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 16) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,16}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124710 Number of base 17 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 17, 49, 113, 301, 797, 2173, 5981, 16645, 46661, 131629, 373181, 1062481, 3035777, 8700601, 25002473, 72015925, 207858677, 601040317, 1740812621, 5049436441, 14666136521, 42649909681, 124166516801, 361855286617
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 17) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,17}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124711 Number of base 18 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 18, 52, 120, 320, 848, 2314, 6374, 17752, 49800, 140582, 398834, 1136270, 3248718, 9316828, 26790080, 77212552, 222993608, 645193126, 1869809474, 5426815810, 15771487250, 45891045208, 133679744924, 389803622998
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 18) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,18}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124712 Number of base 19 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 19, 55, 127, 339, 899, 2455, 6767, 18859, 52939, 149535, 424487, 1210059, 3461659, 9933055, 28577687, 82409179, 238128539, 689345935, 1998806327, 5804195179, 16876837979, 49132180735, 143192973047, 417751959379
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 19) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,19}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124713 Number of base 20 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 20, 58, 134, 358, 950, 2596, 7160, 19966, 56078, 158488, 450140, 1283848, 3674600, 10549282, 30365294, 87605806, 253263470, 733498744, 2127803180, 6181574548, 17982188708, 52373316262, 152706201170, 445700295760
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 20) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,20}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124714 Number of base 21 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 21, 61, 141, 377, 1001, 2737, 7553, 21073, 59217, 167441, 475793, 1357637, 3887541, 11165509, 32152901, 92802433, 268398401, 777651553, 2256800033, 6558953917, 19087539437, 55614451789, 162219429293, 473648632141
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 21) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,21}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124715 Number of base 22 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 22, 64, 148, 396, 1052, 2878, 7946, 22180, 62356, 176394, 501446, 1431426, 4100482, 11781736, 33940508, 97999060, 283533332, 821804362, 2385796886, 6936333286, 20192890166, 58855587316, 171732657416, 501596968522
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 22) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,22}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

A124716 Number of base 23 circular n-digit numbers with adjacent digits differing by 1 or less.

Original entry on oeis.org

1, 23, 67, 155, 415, 1103, 3019, 8339, 23287, 65495, 185347, 527099, 1505215, 4313423, 12397963, 35728115, 103195687, 298668263, 865957171, 2514793739, 7313712655, 21298240895, 62096722843, 181245885539, 529545304903
Offset: 0

Views

Author

R. H. Hardin, Dec 28 2006

Keywords

Comments

[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 23) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,23}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012

Links

Previous Showing 21-30 of 33 results. Next

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