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 23 results. Next

A279570 Number of length n inversion sequences avoiding the patterns 110 and 120.

Original entry on oeis.org

1, 1, 2, 6, 22, 92, 423, 2091, 10950, 60120, 343453, 2029809, 12354661, 77168197, 493189283, 3217459119, 21382723456, 144518555231, 991885282987, 6904454991721, 48691257834999, 347542736059492, 2508603139285095, 18297609829743478, 134772911886028731
Offset: 0

Views

Author

Megan A. Martinez, Feb 21 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k and e_i > e_k. This is the same as the set of length n inversion sequences avoiding 110 and 120.

Examples

			The length 4 inversion sequences avoiding (110,120) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.

Links

Crossrefs

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279571, A279572, A279573.

Extensions

a(10)-a(24) from Alois P. Heinz, Feb 21 2017

A279559 Number of length n inversion sequences avoiding the patterns 010 and 120.

Original entry on oeis.org

1, 1, 2, 5, 15, 52, 201, 845, 3801, 18089, 90316, 470010, 2536077, 14127741, 80966690, 475979359, 2863157581, 17585971037, 110095460224, 701418693025, 4541497543092, 29847982448766, 198913925919741, 1342890255133042, 9176456969273844, 63422002415068463
Offset: 0

Views

Author

Megan A. Martinez, Jan 17 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_k. This is the same as the set of length n inversion sequences avoiding 010 and 120.

Examples

			The length 4 inversion sequences avoiding (010, 120) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A000108, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Extensions

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

A279555 Number of length n inversion sequences avoiding the patterns 110, 210, 120, and 010.

Original entry on oeis.org

1, 1, 2, 5, 15, 51, 189, 746, 3091, 13311, 59146, 269701, 1256820, 5966001, 28773252, 140695923, 696332678, 3483193924, 17589239130, 89575160517, 459648885327, 2374883298183, 12346911196912, 64555427595970, 339276669116222, 1791578092326881, 9501960180835998
Offset: 0

Views

Author

Megan A. Martinez, Dec 16 2016

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, 120, and 210.
It can be shown that this sequence also counts the length n inversion sequences with no entries e_i, e_j, e_k (where i e_j >=e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 100, 120, and 210.
From Andrei Asinowski, Jan 22 2025: (Start)
It also enumerates seven other classes of inversion sequences defined by avoidance of four patterns of length 3 (case 166 in Callan and Mansour).
It also enumerates inversion sequences that avoid the patterns 011 and 201, and inversion sequences that avoid the patterns 011 and 210.
For n >= 1, it also enumerates strong rectangulations that avoid T-shaped joints. (End)

Examples

			The length 3 inversion sequences avoiding (010, 110, 120, 210) are 000, 001, 002, 011, 012.
The length 4 inversion sequences avoiding (010, 110, 120, 210) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Formula

a(n) ~ c * (1 + sqrt(2))^(2*n) / n^(3/2), where c = 0.00391075995650885016134430802... - Vaclav Kotesovec, Jan 23 2025

Extensions

a(10)-a(26) from Alois P. Heinz, Jan 05 2017

A279564 Number of length n inversion sequences avoiding the patterns 000 and 100.

Original entry on oeis.org

1, 1, 2, 5, 16, 60, 260, 1267, 6850, 40572, 260812, 1805646, 13377274, 105487540, 881338060, 7770957903, 72060991394, 700653026744, 7123871583656, 75561097962918, 834285471737784, 9570207406738352, 113855103776348136, 1402523725268921870, 17863056512845724036, 234910502414771617316, 3185732802058088068444, 44501675392317774477088
Offset: 0

Views

Author

Megan A. Martinez, Feb 09 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_j = e_k. This is the same as the set of length n inversion sequences avoiding 000 and 100.

Links

Crossrefs

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Programs

  • Maple
    b:= proc(n, i, m, s) option remember; `if`(n=0, 1, add(
      `if`(j in s, 0, b(n-1, i+1, max(m, j),
      `if`(j<=m, s union {j}, s))), j=1..i))
    end:
a:= n-> b(n, 1, 0, {}):
seq(a(n), n=0..15);  # Alois P. Heinz, Feb 22 2017
  • Mathematica
    b[n_, i_, m_, s_List] := b[n, i, m, s] = If[n == 0, 1, Sum[If[MemberQ[s, j], 0, b[n-1, i+1, Max[m, j], If[j <= m, s ~Union~ {j}, s]]], {j, 1, i}] ]; a[n_] := b[n, 1, 0, {}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jul 10 2017, after Alois P. Heinz *)

Formula

The length 4 inversion sequences avoiding (000,100) are 0011, 0012, 0013, 0021, 0022, 0023, 0101, 0102, 0103, 0110, 0112, 0113, 0120, 0121, 0122, 0123.

Extensions

a(10)-a(23) from Alois P. Heinz, Feb 22 2017
a(24)-a(27) from Vaclav Kotesovec, Oct 08 2021

A279566 Number of length n inversion sequences avoiding the patterns 102 and 201.

Original entry on oeis.org

1, 1, 2, 6, 22, 87, 354, 1465, 6154, 26223, 113236, 494870, 2185700, 9743281, 43784838, 198156234, 902374498, 4131895035, 19012201080, 87864535600, 407664831856, 1898184887679, 8867042353912, 41543375724751, 195164372948152, 919138464708907, 4338701289961694, 20524046955770940
Offset: 0

Views

Author

Megan A. Martinez, Feb 09 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_j < e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 102 and 201.

Examples

			The length 4 inversion sequences avoiding (102, 201) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0100, 0101, 0110, 0111, 0112, 0113, 0120, 0121, 0122, 0123

Links

Crossrefs

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Formula

G.f.: (-8*x^4 + 18*x^3 - 10*x^2 - 8*x + 4 + 2 * (2*x - 1) * (x^2 - 2*x + 2) * ((5*x - 1)*(x - 1))^(1/2)) / (4*x * (2*x - 1) * (x - 1) * (x - 2)^2). - Benjamin Testart, Jul 12 2024
a(n) ~ 41 * 5^(n + 3/2) / (648 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Nov 21 2024

Extensions

a(10)-a(11) from Alois P. Heinz, Feb 24 2017
a(12)-a(17) from Bert Dobbelaere, Dec 30 2018
a(18) and beyond from Benjamin Testart, Jul 12 2024

A279557 Number of length n inversion sequences avoiding the patterns 110, 120, and 021.

Original entry on oeis.org

1, 1, 2, 6, 20, 68, 233, 805, 2807, 9879, 35073, 125513, 452389, 1641029, 5986994, 21954974, 80884424, 299233544, 1111219334, 4140813374, 15478839554, 58028869154, 218123355524, 821908275548, 3104046382352, 11747506651600, 44546351423300, 169227201341652
Offset: 0

Views

Author

Megan A. Martinez, Jan 16 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k and e_i <> e_k. This is the same as the set of length n inversion sequences avoiding 110, 120, and 021.

Examples

			The length 4 inversion sequences avoiding (110, 120, 021) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0022, 0023, 0100, 0101, 0102, 0103, 0111, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A000108, A114277, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<3, n!,
      ((5*n^2-6*n-2)*a(n-1)-(4*n-2)*(n-1)*a(n-2))/(n^2-4))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 11 2017
  • Mathematica
    a[n_] := 1 + Sum[(k - t - 1) (k - t)/(n - t + 1)* Binomial[2 n - k - t + 1, n - k + 1], {t, n - 1}, {k, t + 2, n + 1}]; Array[a, 28, 0] (* Robert G. Wilson v, Feb 25 2017 *)

Formula

a(n) = 1 + Sum_{t=1..n-1} Sum_{k=t+2..n+1} (k-t-1)*(k-t)/(n-t+1) * binomial(2n-k-t+1,n-k+1).
Conjecture: a(n) = C_{n+1}-Sum_{i=1..n} C_i where C_i is the i-th Catalan number, binomial(2i,i)/(i+1).
Assuming the conjecture a(n) ~ (64/3)*4^n/((4*n+7)^(3/2)*sqrt(Pi)). - Peter Luschny, Feb 24 2017
From Alois P. Heinz, Mar 11 2017: (Start)
a(n) = 1 + A114277(n-2) for n>1.
G.f.: (sqrt(1-4*x)+2*x-1)*(2*x-1)/(2*(1-x)*x^2). (End)
D-finite with recurrence: (n+2)*a(n) +(-7*n-4)*a(n-1) +2*(7*n-5)*a(n-2) +4*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Feb 21 2020

Extensions

a(10)-a(12) from Alois P. Heinz, Feb 24 2017
a(13) onward Robert G. Wilson v, Feb 25 2017

A279565 Number of length n inversion sequences avoiding the patterns 100, 110, 120, 201, and 210.

Original entry on oeis.org

1, 1, 2, 6, 21, 81, 332, 1420, 6266, 28318, 130412, 609808, 2887582, 13818590, 66726628, 324713196, 1590853485, 7840315329, 38843186366, 193342353214, 966409013021, 4848846341569, 24412146213116, 123290812268404, 624448756434476, 3171046361310556
Offset: 0

Views

Author

Megan A. Martinez, Feb 09 2017

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k. This is the same as the set of length n inversion sequences avoiding 100, 110, 120, 201, and 210.

Examples

			The length 4 inversion sequences avoiding (100, 110, 120, 201, 210) are 0000, 0001, 0002, 0003, 0010, 0011, 0012, 0013, 0020, 0021, 0022, 0023, 0101, 0102, 0103, 0111, 0112, 0113, 0121, 0122, 0123.

Links

Crossrefs

Cf. A000108, A057552, A263777, A263778, A263779, A263780, A279551, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Programs

  • Magma
    I:=[6, 21, 81]; [1,1,2] cat [n le 3 select I[n] else ( (n+1)*(17*n+6)*Self(n-1) +(49*n^2+11*n+22)*Self(n-2) +3*(3*n-1)*(3*n-2)*Self(n-3) )/(5*(n+2)*(n+1)) : n in [1..30]]; // G. C. Greubel, Mar 29 2019
  • Maple
    a:= proc(n) option remember; `if`(n<3, n!,
      ((n-1)*(17*n-28)*a(n-1) +(49*n^2-185*n+196)*a(n-2)
       +(3*(3*n-7))*(3*n-8)*a(n-3)) / (5*n*(n-1)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 22 2017
  • Mathematica
    a[n_] := a[n] = If[n < 3, n!, (((n - 1)*(17*n - 28)*a[n-1] + (49*n^2 - 185*n + 196)*a[n-2] + (3*(3*n - 7))*(3*n - 8)*a[n-3]) / (5*n*(n - 1)))]; Array[a, 30, 0] (* Jean-François Alcover, Nov 06 2017, after Alois P. Heinz *)
Join[{1}, Table[(1/n)*Sum[m*Sum[Binomial[k, n-m-k]*Binomial[n+k-1, k], {k, 0, n-m}], {m, 1, n}], {n, 1, 30}]] (* G. C. Greubel, Mar 29 2019 *)
  • Maxima
    a(n):=if n=0 then 1 else sum(m*sum(binomial(k,n-m-k)*binomial(n+k-1,k),k,0,n-m),m,1,n)/n; /* Vladimir Kruchinin, Mar 26 2019 */
  • PARI
    my(x='x+O('x^30)); Vec(round(3/(4-4*sin(asin((27*x+11)/16)/3)))) \\ G. C. Greubel, Mar 29 2019
  • Sage
    [1] +[(1/n)*(sum(sum(k*binomial(j,n-k-j)*binomial(n+j-1,j) for j in (0..n-k)) for k in (1..n))) for n in (1..30)] # G. C. Greubel, Mar 29 2019

Formula

G.f.: 3/(4-4*sin(asin((27*x+11)/16)/3)). - Vladimir Kruchinin, Mar 25 2019
a(n) = (1/n)*Sum_{m=1..n} m*Sum_{k=0..n-m} C(k,n-m-k)*C(n+k-1,k), n>0, a(0)=1. - Vladimir Kruchinin, Mar 26 2019
a(n) ~ 3^(3*n + 1/2) / (2^(7/2) * sqrt(Pi) * n^(3/2) * 5^(n - 1/2)). - Vaclav Kotesovec, Oct 07 2021
Conjecture: a(n) = (v_n + v_{n+1})/2 for n > 0 with a(0) = 1 where we start with vector v of fixed length m with elements v_i = 1 and for i=1..m-2, for j=i+2..m apply v_j := Sum_{k=0..2} v_{j-k}. - Mikhail Kurkov, Sep 03 2024

Extensions

a(10)-a(25) from Alois P. Heinz, Feb 22 2017

A279552 Number of length n inversion sequences avoiding the patterns 000 and 010.

Original entry on oeis.org

1, 1, 2, 4, 10, 29, 95, 345, 1376, 5966, 27886, 139608, 744552, 4210191, 25140790, 157981820, 1041480482, 7183374125, 51711299169, 387683162541, 3020997261596, 24424884853963, 204559337781097, 1772011400733378, 15855597322378302, 146360032952969570
Offset: 0

Views

Author

Megan A. Martinez, Dec 15 2016

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_k and e_i = e_k. This is the same as the set of length n inversion sequences avoiding 000 and 010.

Examples

			For n=3, the inversion sequences are 001, 002, 011, 012.
For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Extensions

a(10)-a(20) from Alois P. Heinz, Feb 23 2017
a(21) onwards from Benjamin Testart, Feb 01 2023

A279551 Number of length n inversion sequences avoiding the patterns 000, 010, 110, and 120.

Original entry on oeis.org

1, 1, 2, 4, 10, 27, 79, 247, 816, 2822, 10158, 37875, 145695, 576288, 2337412, 9698820, 41089107, 177424188, 779699793, 3482575169, 15791709187, 72621800171, 338388714955, 1596314968112, 7618218238583, 36756086159343, 179176803145900, 882002961543492
Offset: 0

Views

Author

Megan A. Martinez, Dec 15 2016

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i= e_k. This is the same as the set of length n inversion sequences avoiding 000, 010, 110, and 120.

Examples

			For n=3, the inversion sequences are 001, 002, 011, 012.
For n=4, the inversion sequences are 0011, 0012, 0013, 0021, 0022, 0023, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279552, A279553, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Extensions

Typo in comment corrected and a(10)-a(27) added by Alois P. Heinz, Feb 22 2017

A279553 Number of length n inversion sequences avoiding the patterns 110, 210, 120, 201, and 010.

Original entry on oeis.org

1, 1, 2, 5, 15, 50, 178, 663, 2552, 10071, 40528, 165682, 686151, 2872576, 12137278, 51690255, 221657999, 956265050, 4147533262, 18074429421, 79102157060, 347519074010, 1532070899412, 6775687911920, 30052744139440, 133649573395725, 595816470717728
Offset: 0

Views

Author

Megan A. Martinez, Dec 15 2016

Keywords

Comments

A length n inversion sequence e_1e_2...e_n is a sequence of integers where 0 <= e_i <= i-1. The term a(n) counts those length n inversion sequences with no entries e_i, e_j, e_k (where i e_k and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 110, 120, 201, and 210.
It can be shown that this sequence also counts the length n inversion sequences with no entries e_i, e_j, e_k (where i e_j and e_i >= e_k. This is the same as the set of length n inversion sequences avoiding 010, 100, 120, 201, and 210.

Examples

			The length 3 inversion sequences avoiding (110, 210, 120, 201, 010) are 000, 001, 002, 011, 012.
The length 4 inversion sequences avoiding (110, 210, 120, 201, 010) are 0000, 0001, 0002, 0003, 0011, 0012, 0013, 0021, 0022, 0023, 0111, 0112, 0113, 0122, 0123.

Links

Crossrefs

Cf. A263777, A263778, A263779, A263780, A279551, A279552, A279554, A279555, A279556, A279557, A279558, A279559, A279560, A279561, A279562, A279563, A279564, A279565, A279566, A279567, A279568, A279569, A279570, A279571, A279572, A279573.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n<4, [1, 1, 2, 5][n+1],
      ((12*(n-1))*(182*n^3-1659*n^2+4628*n-3756)*a(n-1)
      -(4*(91*n^4-1057*n^3+3812*n^2-4046*n-906))*a(n-2)
      +(6*(n-4))*(182*n^3-1659*n^2+4901*n-4630)*a(n-3)
      -(4*(n-4))*(n-5)*(91*n^2-511*n+690)*a(n-4))
       /(5*n*(n-1)*(91*n^2-693*n+1292)))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 22 2017
  • Mathematica
    a[n_] := a[n] = If[n < 4, {1, 1, 2, 5}[[n + 1]], ((12*(n - 1))*(182*n^3 - 1659*n^2 + 4628*n - 3756)*a[n - 1] - (4*(91*n^4 - 1057*n^3 + 3812*n^2 - 4046*n - 906))*a[n - 2] + (6*(n - 4))*(182*n^3 - 1659*n^2 + 4901*n - 4630)*a[n - 3] - (4*(n - 4))*(n - 5)*(91*n^2 - 511*n + 690)*a[n - 4]) / (5*n*(n - 1)*(91*n^2 - 693*n + 1292))]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 06 2017, after Alois P. Heinz *)
  • PARI
    seq(N) = my(x='x+O('x^N)); Vec(1+serreverse((-x^3+x^2+x)/(2*x^2+3*x+1)));
seq(27) \\ Gheorghe Coserea, Jul 11 2018

Formula

G.f.: 1 + Series_Reversion(x*A094373(-x)). - Gheorghe Coserea, Jul 11 2018
a(n) ~ c * d^n / (sqrt(Pi) * n^(3/2)), where d = 4.730576939379622099763633264641101585205420756515858657461873... is the greatest real root of the equation 4 - 12*d + 4*d^2 - 24*d^3 + 5*d^4 = 0 and c = 0.3916760466183576202289779130261876915536170330427700961416097... is the positive real root of the equation -5 - 64*c^2 - 33728*c^4 + 209664*c^6 + 93184*c^8 = 0. - Vaclav Kotesovec, Jul 12 2018
D-finite with recurrence: 45*n*(n-1)*a(n) -4*(n-1)*(49*n-66)*a(n-1) +2*(-25*n^2+157*n-264)*a(n-2) +2*(-70*n^2+445*n-714)*a(n-3) -4*(n-6)*(n-13)*a(n-4) -4*(n-6)*(2*n-17)*a(n-5) +8*(n-6)*(n-7)*a(n-6)=0. - R. J. Mathar, Feb 21 2020

Extensions

a(10)-a(16) from Lars Blomberg, Feb 02 2017
a(17)-a(26) from Alois P. Heinz, Feb 22 2017
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