A078495 -id:A078495 - cp's OEIS frontend

A268199 Somos's sequence {b(3,n)} defined in comment in A078495: a(0)=a(1)=...=a(8)=1; for n>=9, a(n)=(a(n-1)a(n-8)+a(n-4)a(n-5))/a(n-9).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 13, 25, 45, 125, 233, 419, 805, 2252, 8343, 23554, 55889, 195533, 514781, 1769117, 6540689, 31873013, 162776741, 568710437, 1840702289, 10169970946, 53308101423, 363030298268, 1933899726085, 12286029791291

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 16 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..292

Cf. A006721, A078495, A271948.

[n le 9 select 1 else (Self(n-1)*Self(n-8) + Self(n-4)*Self(n-5)) /Self(n-9): n in [1..40]]; // G. C. Greubel, Feb 21 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[3,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 16 2016 *)
a[ n_] := a[n] = Which[ n<0, a[8-n], n<9, 1, True, (a[n - 1] a[n - 8] + a[n - 4] a[n - 5]) / a[n - 9]]; (* Michael Somos, Nov 16 2016 *)

{a(n) = if(n<= 8, 1, (a(n-1)*a(n-8)+a(n-4)*a(n-5))/a(n-9))};
for(n=1,40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

a(n) = a(8-n) for all n in Z. - Michael Somos, Nov 16 2016

A271949 Somos's sequence {b(4,n)} defined in comment in A078495: a(0)=a(1)=...=a(10)=1; for n>=11, a(n)=(a(n-1)a(n-10)+a(n-5)a(n-6))/a(n-11).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 14, 26, 46, 76, 200, 356, 596, 1044, 1952, 5136, 17888, 48376, 109520, 225248, 724672, 1749280, 5359328, 18277312, 57803136, 235710976, 1067767168, 3411743616, 9748806656, 29696723456, 156028988416

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..343

Cf. A006721, A078495, A268199, A271948.

[n le 11 select 1 else (Self(n-1)*Self(n-10) + Self(n-5)*Self(n- 6))/Self(n-11): n in [1..30]]; // G. C. Greubel, Feb 21 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[4,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
RecurrenceTable[{Table[a[d]==1,{d,0,10}],a[n]==(a[n-1]a[n-10]+ a[n-5]a[n-6])/ a[n-11]},a,{n,50}] (* Harvey P. Dale, Oct 18 2021 *)

{a(n) = if(n< 11, 1, (a(n-1)*a(n-10) + a(n-5)*a(n-6))/a(n-11))};
for(n=0,30, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

A271950 Somos's sequence {b(5,n)} defined in comment in A078495: a(0)=a(1)=...=a(12)=1; for n>=13, a(n)=(a(n-1)a(n-12)+a(n-6)a(n-7))/a(n-13).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 15, 27, 47, 77, 119, 301, 519, 827, 1351, 2345, 4263, 10598, 35021, 91652, 200923, 396578, 742721, 2258305, 5126953, 14354017, 45716169, 138331649, 377080865, 1330892225, 5490413305, 16470110241

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..392

Cf. A006721, A078495, A268199, A271948, A271949.

[n le 13 select 1 else ((Self(n-1)*Self(n-12) + Self(n-6)*Self(n- 7) )/Self(n-13)): n in [1..40]]; // G. C. Greubel, Feb 21 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[5,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]== a[8]== a[9]== a[10]== a[11] ==a[12]==1,a[n]==(a[n-1]a[n-12]+a[n-6]a[n-7])/a[n-13]},a,{n,50}] (* Harvey P. Dale, May 01 2018 *)

{a(n) = if(n< 12, 1, (a(n-1)*a(n-12) + a(n-6)*a(n-7))/a(n-13))};
for(n=0,40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

A271952 Somos's sequence {b(6,n)} defined in comment in A078495: a(0)=a(1)=...=a(14)=1; for n>=15, a(n)=(a(n-1)a(n-14)+a(n-7)a(n-8))/a(n-15).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 10, 16, 28, 48, 78, 120, 176, 432, 728, 1120, 1736, 2832, 4864, 8576, 20224, 63808, 162624, 348224, 668288, 1204736, 2114560, 6175744, 13394432, 34860544, 104595968, 304683008, 807587840

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..440

Cf. A006721, A078495, A268199, A271948, A271949, A271950.

[n le 15 select 1 else (Self(n-1)*Self(n-14)+Self(n-7)*Self(n-8))/Self(n-15): n in [1..60]]; // G. C. Greubel, Jul 30 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[6,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)

{a(n) = if(n<= 15, 1, (a(n-1)*a(n-14) + a(n-7)*a(n-8))/a(n-15))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A271954 Somos's sequence {b(7,n)} defined in comment in A078495: a(0)=a(1)=...=a(16)=1; for n>=17, a(n)=(a(n-1)a(n-16)+a(n-8)a(n-9))/a(n-17).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 17, 29, 49, 79, 121, 177, 249, 597, 989, 1483, 2209, 3425, 5589, 9447, 16137, 36240, 109683, 273382, 574885, 1081260, 1898415, 3213378, 5381793, 15251949, 31924773, 78189885

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..487

Cf. A006721, A078495, A268199, A271948, A271949, A271950, A271952.

[n le 17 select 1 else (Self(n-1)*Self(n-16)+Self(n-8)*Self(n-9))/Self(n-17): n in [1..60]]; // G. C. Greubel, Jul 30 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[7,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)

{a(n) = if(n<= 17, 1, (a(n-1)*a(n-16) + a(n-8)*a(n-9))/a(n-17))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A271955 Somos's sequence {b(8,n)} defined in comment in A078495: a(0)=a(1)=...=a(18)=1; for n>=19, a(n)=(a(n-1)a(n-18)+a(n-9)a(n-10))/a(n-19).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 30, 50, 80, 122, 178, 250, 340, 800, 1308, 1924, 2780, 4136, 6452, 10476, 17348, 28720, 61664, 179696, 439304, 910464, 1686704, 2905792, 4793624, 7753616, 12537856

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 17 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..533

Cf. A006721, A078495, A268199, A271948, A271949, A271950, A271952, A271954.

[n le 19 select 1 else (Self(n-1)*Self(n-18)+Self(n-9)*Self(n-10))/Self(n-19): n in [1..60]]; // G. C. Greubel, Jul 30 2018

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[8,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 17 2016 *)

{a(n) = if(n<= 19, 1, (a(n-1)*a(n-18) + a(n-9)*a(n-10))/a(n-19))}; for(n=1,50, print1(a(n), ", ")) \\ G. C. Greubel, Jul 30 2018

A272038 Somos's sequence {b(9,n)} defined in comment in A078495: a(0)=a(1)=...=a(20)=1; for n>=21, a(n)=(a(n-1)a(n-20)+a(n-10)a(n-11))/a(n-21).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 19, 31, 51, 81, 123, 179, 251, 341, 451, 1045, 1691, 2451, 3459, 4977, 7467, 11679, 18755, 30349, 48763, 100474, 282777, 679512, 1391391, 2547414, 4327101

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Apr 18 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..578

Cf. A006721, A078495, A268199, A271954, A271948, A271949, A271950, A271952, A271955.

def b(k, n)
  b = Array.new(2 * k + 3, 1)
  (2 * k + 3..n).each{|i|
    j = (b[i - 1] * b[i - 2 * k - 2] + b[i - k - 1] * b[i - k - 2]) / b[i - 2 * k - 3].to_r
    j = j.to_i if j.denominator == 1
    b[i] = j
  }
  b[0..n]
end
p b(9, n) # Seiichi Manyama, May 04 2016

A006723 Somos-7 sequence: a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-5) + a(n-3) * a(n-4)) / a(n-7), a(0) = ... = a(6) = 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 3, 5, 9, 17, 41, 137, 769, 1925, 7203, 34081, 227321, 1737001, 14736001, 63232441, 702617001, 8873580481, 122337693603, 1705473647525, 22511386506929, 251582370867257, 9254211194697641, 215321535159114017

Offset: 0

N. J. A. Sloane

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=0..100
R. H. Buchholz and R. L. Rathbun, An infinite set of Heron triangles with two rational medians, Amer. Math. Monthly, 104 (1997), 107-115.
Chang, Xiangke; Hu, Xingbiao, A conjecture based on Somos-4 sequence and its extension, Linear Algebra Appl. 436, No. 11, 4285-4295 (2012).
S. Fomin and A. Zelevinsky, The Laurent phenomenon, arXiv:math/0104241 [math.CO], 2001.
David Gale, The strange and surprising saga of the Somos sequences, Math. Intelligencer 13(1) (1991), pp. 40-42.
R. W. Gosper and Richard C. Schroeppel, Somos Sequence Near-Addition Formulas and Modular Theta Functions, arXiv:math/0703470 [math.NT], 2007.
J. L. Malouf, An integer sequence from a rational recursion, Discr. Math. 110 (1992), 257-261.
J. Propp, The Somos Sequence Site
R. M. Robinson, Periodicity of Somos sequences, Proc. Amer. Math. Soc., 116 (1992), 613-619.
Vladimir Shevelev and Peter J. C. Moses, On a sequence of polynomials with hypothetically integer coefficients, arXiv preprint arXiv:1112.5715 [math.NT], 2011.
Michael Somos, Somos 7 Sequence
Michael Somos, Brief history of the Somos sequence problem
Alex Stone, The Astonishing Behavior of Recursive Sequences, Quanta Magazine, Nov 16 2023, 13 pages.
A. van der Poorten, Hyperelliptic curves, continued fractions and Somos sequences, arXiv:math/0608247 [math.NT], 2006.
Eric Weisstein's World of Mathematics, Somos Sequence.
Index entries for two-way infinite sequences

Cf. A006720, A006721, A006722, A048736.

Cf. A078495.

a006723 n = a006723_list !! n
a006723_list = [1,1,1,1,1,1,1] ++
  zipWith div (foldr1 (zipWith (+)) (map b [1..3])) a006723_list
  where b i = zipWith (*) (drop i a006723_list) (drop (7-i) a006723_list)
-- Reinhard Zumkeller, Jan 22 2012

I:=[1,1,1,1,1,1,1]; [n le 7 select I[n] else (Self(n-1)*Self(n-6) + Self(n-2)*Self(n-5) + Self(n-3)*Self(n-4))/Self(n-7): n in [1..30]]; // G. C. Greubel, Feb 21 2018

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==1,a[n] == (a[n-1]a[n-6]+a[n-2]a[n-5]+a[n-3]a[n-4])/a[n-7]},a,{n,30}] (* Harvey P. Dale, Jan 19 2012 *)

{a(n) = my(v); if( n<0, n = 6-n); if( n<7, 1, n++; v = vector(n, k, 1); for( k=8, n, v[k] = (v[k-1] * v[k-6] + v[k-2] * v[k-5] + v[k-3] * v[k-4]) / v[k-7]); v[n])};

from gmpy2 import divexact
A006723 = [1,1,1,1,1,1,1]
for n in range(7,101):
    A006723.append(divexact(A006723[n-1]*A006723[n-6]+A006723[n-2]*A006723[n-5]+A006723[n-3]*A006723[n-4],A006723[n-7]))
# Chai Wah Wu, Sep 01 2014

a(6 - n) = a(n) for all n in Z.

a(n) = ((8-2*(-1)^n)*a(n-5)*a(n-3)-a(n-4)^2)/a(n-8). - Bruno Langlois, Aug 09 2016

More terms from James A. Sellers, Aug 22 2000

A060656 a(n) = 2a(n-1)a(n-2)/a(n-3), with a(0)=a(1)=1.

Original entry on oeis.org

1, 1, 2, 4, 16, 64, 512, 4096, 65536, 1048576, 33554432, 1073741824, 68719476736, 4398046511104, 562949953421312, 72057594037927936, 18446744073709551616, 4722366482869645213696, 2417851639229258349412352

Offset: 0

Henry Bottomley, Apr 18 2001

a(n+1) is the Hankel transform of A135052. - Paul Barry, Nov 15 2007
a(n+1) is the Hankel transform of the aerated large Schroeder numbers. a(n) and a(n+1) both satisfy the trivial Somos-4 recurrence u(n)=4*u(n-2)^2/u(n-4). Associated with the elliptic curve y^2=1-6x^2+x^4 via Schroeder numbers. - Paul Barry, Dec 08 2009
Hankel transform of A089324. - Paul Barry, Mar 01 2010
a(n+1) is the number of n X n binary matrices that are symmetric about both diagonals (bisymmetric). For the derivation of this result, see the link below. - Dennis P. Walsh, Apr 03 2014
1 followed by {a(n-1)}A078495).%20-%20_Vladimir%20Shevelev">(n>=1) is the Somos-3 sequence: b(0)=b(1)=b(2)=1;for n>=3, b(n)=2*b(n-1)*b(n-2)/b(n-3) (cf. comment in A078495). - _Vladimir Shevelev, Apr 20 2016
If the Hankel transform is defined as in the link 'Sequence transformations' then a(n) is the Hankel transform of A151374. - Peter Luschny, Nov 30 2016

			a(6) = 2*64*16/4 = 512.
G.f. = 1 + x + 2*x^2 + 4*x^3 + 16*x^4 + 64*x^5 + 512*x^6 + 4096*x^7 + ...

Harry J. Smith, Table of n, a(n) for n = 0..100
Peter Luschny, Sequence transformations
Dennis P. Walsh, Notes on binary bisymmetric matrices

Cf. A002416, A002620, A016116, A038754, A089324, A135052, A262666, A078495, A151374.

A060656:=n->2^floor(n^2/4); seq(A060656(n), n=0..20); # Wesley Ivan Hurt, Apr 30 2014

a[ n_] := 2^Quotient[n^2, 4]; (* Michael Somos, Jan 24 2014 *)
nxt[{a_,b_,c_}]:={b,c,(2c*b)/a}; NestList[nxt,{1,1,2},20][[All,1]] (* Harvey P. Dale, Nov 26 2017 *)

{ for (n=0, 100, write("b060656.txt", n, " ", 2^(n^2\4)); ) } \\ Harry J. Smith, Jul 09 2009

{a(n) = 2^(n^2\4)}; /* Michael Somos, Jan 24 2014 */

a(n) = 2^floor( n^2/4 ) = a(n - 1) * 2^floor( n/2 ) = a(n - 2) * 2^(n - 1) = a(n - 1) * A016116(n) = 2^A002620(n).
0 = a(n) * a(n+3) + a(n+1) * ( -2*a(n+2) ) for all n in Z. - Michael Somos, Jan 24 2014
0 = a(n) * a(n+4) + a(n+2) * ( -4*a(n+2) ) for all n in Z. - Michael Somos, Jan 24 2014

A025795 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)).

Original entry on oeis.org

1, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 21, 23, 24, 25, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 42, 43, 45, 47, 48, 51, 52, 54, 56, 58, 60, 62, 64, 66, 68, 71, 72, 75, 77, 79, 82, 84, 86, 89, 91, 94, 96, 99, 101, 104

Offset: 0

N. J. A. Sloane

a(n) is the number of ways to pay n dollars with coins of two, three and five dollars. E.g., a(0)=1 because there is one way to pay: with no coin; a(1)=0 no possibility; a(2)=1 (2=1*2); a(3)=1 (3=1*3); a(4)=1 (4=2*2) a(5)=2 (5=3+2=1*5) ... - Richard Choulet, Jan 20 2008

a(n) is the number of partitions of n into parts 2, 3, and 5. See the preceding comment by R. Choulet. - Wolfdieter Lang, Mar 15 2012

			G.f. = 1 + x^2 + x^3 + x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 3*x^8 + 3*x^9 + 4*x^10 + ...

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Milan Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,-1,-1,0,1).

Cf. A008676, A078495, A103221.

a[ n_] := Quotient[n^2 + 10 n + 1 - 13 Mod[n, 2], 60] + 1; (* Michael Somos, Nov 17 2017 *)

{a(n) = (n^2 + 10*n + 1 - n%2 * 13) \60 + 1} /* Michael Somos, Feb 05 2008 */

G.f.: 1/((1-x^2)*(1-x^3)*(1-x^5)).
Let [b(1); b(2); ...; b(p)] denote a periodic sequence: e.g., [0; 1] defines the sequence c such that c(0)=c(2)=...=c(2*k)=0 and c(1)=c(3)=...=c(2*k+1)=1. Then a(n)=0.25*[0; 1] - (1/3)*[1; 0; 0] + (1/5)*[0; 1; 1; 0; 3] + ((n+1)*(n+2)/60) + (7*(n+1)/60). - Richard Choulet, Jan 20 2008
If ||A|| is the nearest number to A (A not a half-integer) we also have a(n) = ||((n+1)*(n+9)/60) + (1/5)[0; 1; 1; 0; 3]. - Richard Choulet, Jan 20 2008
a(n) = 77/360 + 7*(n+1)/60 + (n+2)*(n+1)/60 + (-1)^n/8 - (2/9)*cos(2*(n+2)*Pi/3) + (4/(5*sqrt(5)+25))*cos(2*n*Pi/5) - (4/(5*sqrt(5)-25))*cos(4*n*Pi/5). - Richard Choulet, Jan 20 2008
Euler transform of length 5 sequence [0, 1, 1, 0, 1]. - Michael Somos, Feb 05 2008
a(n) = a(-10-n) for all n in Z. - Michael Somos, Feb 25 2008
a(n) - a(n-2) = A008676(n). a(n) - a(n-5) = A103221(n) = A008615(n+2). A078495(n) = 2^(a(n-7) + a(n-9)) * 3^a(n-8) for all n in Z. - Michael Somos, Nov 17 2017, corrected Jun 23 2021
a(n)-a(n-3) = A008616(n). - R. J. Mathar, Jun 23 2021
a(n) = floor((n^2 + 10*n + 6*(9+(-1)^n))/60). - Hoang Xuan Thanh, Jun 15 2025

cp's OEIS Frontend

A268199 Somos's sequence {b(3,n)} defined in comment in A078495: a(0)=a(1)=...=a(8)=1; for n>=9, a(n)=(a(n-1)*a(n-8)+a(n-4)*a(n-5))/a(n-9).

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A271949 Somos's sequence {b(4,n)} defined in comment in A078495: a(0)=a(1)=...=a(10)=1; for n>=11, a(n)=(a(n-1)*a(n-10)+a(n-5)*a(n-6))/a(n-11).

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A271950 Somos's sequence {b(5,n)} defined in comment in A078495: a(0)=a(1)=...=a(12)=1; for n>=13, a(n)=(a(n-1)*a(n-12)+a(n-6)*a(n-7))/a(n-13).

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A271952 Somos's sequence {b(6,n)} defined in comment in A078495: a(0)=a(1)=...=a(14)=1; for n>=15, a(n)=(a(n-1)*a(n-14)+a(n-7)*a(n-8))/a(n-15).

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A271954 Somos's sequence {b(7,n)} defined in comment in A078495: a(0)=a(1)=...=a(16)=1; for n>=17, a(n)=(a(n-1)*a(n-16)+a(n-8)*a(n-9))/a(n-17).

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Magma

Mathematica

PARI

A271955 Somos's sequence {b(8,n)} defined in comment in A078495: a(0)=a(1)=...=a(18)=1; for n>=19, a(n)=(a(n-1)*a(n-18)+a(n-9)*a(n-10))/a(n-19).

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Magma

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A272038 Somos's sequence {b(9,n)} defined in comment in A078495: a(0)=a(1)=...=a(20)=1; for n>=21, a(n)=(a(n-1)*a(n-20)+a(n-10)*a(n-11))/a(n-21).

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Ruby

A006723 Somos-7 sequence: a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-5) + a(n-3) * a(n-4)) / a(n-7), a(0) = ... = a(6) = 1.

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Haskell

Magma

A268199 Somos's sequence {b(3,n)} defined in comment in A078495: a(0)=a(1)=...=a(8)=1; for n>=9, a(n)=(a(n-1)a(n-8)+a(n-4)a(n-5))/a(n-9).

A271949 Somos's sequence {b(4,n)} defined in comment in A078495: a(0)=a(1)=...=a(10)=1; for n>=11, a(n)=(a(n-1)a(n-10)+a(n-5)a(n-6))/a(n-11).

A271950 Somos's sequence {b(5,n)} defined in comment in A078495: a(0)=a(1)=...=a(12)=1; for n>=13, a(n)=(a(n-1)a(n-12)+a(n-6)a(n-7))/a(n-13).

A271952 Somos's sequence {b(6,n)} defined in comment in A078495: a(0)=a(1)=...=a(14)=1; for n>=15, a(n)=(a(n-1)a(n-14)+a(n-7)a(n-8))/a(n-15).

A271954 Somos's sequence {b(7,n)} defined in comment in A078495: a(0)=a(1)=...=a(16)=1; for n>=17, a(n)=(a(n-1)a(n-16)+a(n-8)a(n-9))/a(n-17).

A271955 Somos's sequence {b(8,n)} defined in comment in A078495: a(0)=a(1)=...=a(18)=1; for n>=19, a(n)=(a(n-1)a(n-18)+a(n-9)a(n-10))/a(n-19).

A272038 Somos's sequence {b(9,n)} defined in comment in A078495: a(0)=a(1)=...=a(20)=1; for n>=21, a(n)=(a(n-1)a(n-20)+a(n-10)a(n-11))/a(n-21).

A060656 a(n) = 2a(n-1)a(n-2)/a(n-3), with a(0)=a(1)=1.

A025795 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)).