A005710 -id:A005710 - cp's OEIS frontend

A058364 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 9 sites wide.

1, 1, 1, 1, 1, 1, 1, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 28, 39, 51, 64, 78, 93, 109, 126, 144, 172, 211, 262, 326, 404, 497, 606, 732, 876, 1048, 1259, 1521, 1847, 2251, 2748, 3354, 4086, 4962, 6010, 7269, 8790, 10637, 12888, 15636, 18990, 23076, 28038

Offset: 1

Yong Kong (ykong(AT)curagen.com), Dec 17 2000

nonn

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 1...m-1, a(m) = m+1. The generating function is (x+m*x^m)/(1-x-x^m). Also a(n) = 1 + n*Sum_{i=1..n/m} binomial(n-1-(m-1)*i, i-1)/i. This gives the number of ways to cover (without overlapping) a ring lattice (or necklace) of n sites with molecules that are m sites wide. Special cases: m=2: A000204, m=3: A001609, m=4: A014097, m=5: A058368, m=6: A058367, m=7: A058366, m=8: A058365, m=9: A058364.

			a(9) = 10 because there is one way to put zero molecule to the necklace and 9 ways to put one molecule.

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.

Cf. A000079, A003269, A003520, A005708, A005709, A005710.

a(n) = 1 + n*sum(binomial(n-1-8*i, i-1)/i, i=1..n/9). a(n) = a(n-1) + a(n-9), a(n) = 1 for n = 1..8, a(9) = 10. generating function = (x+9*x^9)/(1-x-x^9).

A058365 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 8 sites wide.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 9, 10, 11, 12, 13, 14, 15, 16, 25, 35, 46, 58, 71, 85, 100, 116, 141, 176, 222, 280, 351, 436, 536, 652, 793, 969, 1191, 1471, 1822, 2258, 2794, 3446, 4239, 5208, 6399, 7870, 9692, 11950, 14744, 18190, 22429, 27637, 34036, 41906

Offset: 1

Yong Kong (ykong(AT)curagen.com), Dec 17 2000

nonn

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 1...m-1, a(m) = m+1. The generating function is (x+m*x^m)/(1-x-x^m). Also a(n) = 1 + n*Sum_{i=1..n/m} binomial(n-1-(m-1)*i, i-1)/i. This gives the number of ways to cover (without overlapping) a ring lattice (or necklace) of n sites with molecules that are m sites wide. Special cases: m=2: A000204, m=3: A001609, m=4: A014097, m=5: A058368, m=6: A058367, m=7: A058366, m=8: A058365, m=9: A058364.

			a(8) = 9 because there is one way to put zero molecule to the necklace and 8 ways to put one molecule.

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.

Cf. A000079, A003269, A003520, A005708, A005709, A005710.

a(n) = 1 + n*sum(binomial(n-1-7*i, i-1)/i, i=1..n/8). a(n) = a(n-1) + a(n-8), a(n) = 1 for n = 1..7, a(8) = 9. generating function = (x+8*x^8)/(1-x-x^8).

A058366 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 7 sites wide.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 8, 9, 10, 11, 12, 13, 14, 22, 31, 41, 52, 64, 77, 91, 113, 144, 185, 237, 301, 378, 469, 582, 726, 911, 1148, 1449, 1827, 2296, 2878, 3604, 4515, 5663, 7112, 8939, 11235, 14113, 17717, 22232, 27895, 35007, 43946, 55181, 69294, 87011

Offset: 1

Yong Kong (ykong(AT)curagen.com), Dec 17 2000

nonn

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 1...m-1, a(m) = m+1. The generating function is (x+m*x^m)/(1-x-x^m). Also a(n) = 1 + n*Sum_{i=1..n/m} binomial(n-1-(m-1)*i, i-1)/i. This gives the number of ways to cover (without overlapping) a ring lattice (or necklace) of n sites with molecules that are m sites wide. Special cases: m=2: A000204, m=3: A001609, m=4: A014097, m=5: A058368, m=6: A058367, m=7: A058366, m=8: A058365, m=9: A058364.

			a(7) = 8 because there is one way to put zero molecule to the necklace and 7 ways to put one molecule.

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.

Cf. A000079, A003269, A003520, A005708, A005709, A005710.

a(n) = 1 + n*sum(binomial(n-1-6*i, i-1)/i, i=1..n/7). a(n) = a(n-1) + a(n-7), a(n) = 1 for n = 1..6, a(7) = 8. generating function = (x+7*x^7)/(1-x-x^7).

A058367 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 6 sites wide.

Original entry on oeis.org

1, 1, 1, 1, 1, 7, 8, 9, 10, 11, 12, 19, 27, 36, 46, 57, 69, 88, 115, 151, 197, 254, 323, 411, 526, 677, 874, 1128, 1451, 1862, 2388, 3065, 3939, 5067, 6518, 8380, 10768, 13833, 17772, 22839, 29357, 37737, 48505, 62338, 80110, 102949, 132306, 170043, 218548

Offset: 1

Yong Kong (ykong(AT)curagen.com), Dec 17 2000

nonn

This comment covers a family of sequences which satisfy a recurrence of the form a(n) = a(n-1) + a(n-m), with a(n) = 1 for n = 1...m-1, a(m) = m+1. The generating function is (x+m*x^m)/(1-x-x^m). Also a(n) = 1 + n*Sum_{i=1..n/m} binomial(n-1-(m-1)*i, i-1)/i. This gives the number of ways to cover (without overlapping) a ring lattice (or necklace) of n sites with molecules that are m sites wide. Special cases: m=2: A000204, m=3: A001609, m=4: A014097, m=5: A058368, m=6: A058367, m=7: A058366, m=8: A058365, m=9: A058364.

			a(6) = 7 because there is one way to put zero molecule to the necklace and 6 ways to put one molecule.

E. Di Cera and Y. Kong, Theory of multivalent binding in one and two-dimensional lattices, Biophysical Chemistry, Vol. 61 (1996), pp. 107-124.
Y. Kong, General recurrence theory of ligand binding on a three-dimensional lattice, J. Chem. Phys. Vol. 111 (1999), pp. 4790-4799.

Cf. A000079, A003269, A003520, A005708, A005709, A005710.

a(n) = 1 + n*sum(binomial(n-1-5*i, i-1)/i, i=1..n/6). a(n) = a(n-1) + a(n-6), a(n) = 1 for n = 1..5, a(6) = 7. generating function = (x+6*x^6)/(1-x-x^6).

A141539 Square array A(n,k) of numbers of length n binary words with at least k "0" between any two "1" digits (n,k >= 0), read by antidiagonals.

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 1, 2, 3, 8, 1, 2, 3, 5, 16, 1, 2, 3, 4, 8, 32, 1, 2, 3, 4, 6, 13, 64, 1, 2, 3, 4, 5, 9, 21, 128, 1, 2, 3, 4, 5, 7, 13, 34, 256, 1, 2, 3, 4, 5, 6, 10, 19, 55, 512, 1, 2, 3, 4, 5, 6, 8, 14, 28, 89, 1024, 1, 2, 3, 4, 5, 6, 7, 11, 19, 41, 144, 2048, 1, 2, 3, 4, 5, 6, 7, 9, 15, 26, 60, 233, 4096

Offset: 0

Alois P. Heinz, Aug 15 2008

A(n,k+1) = A(n,k) - A143291(n,k).
From Gary W. Adamson, Dec 19 2009: (Start)
Alternative method generated from variants of an infinite lower triangle T(n) = A000012 = (1; 1,1; 1,1,1; ...) such that T(n) has the leftmost column shifted up n times. Then take lim_{k->infinity} T(n)^k, obtaining a left-shifted vector considered as rows of an array (deleting the first 1) as follows:
  1, 2, 4, 8, 16, 32, 64, 128, 256, ... = powers of 2
  1, 1, 2, 3,  5,  8, 13,  21,  34, ... = Fibonacci numbers
  1, 1, 1, 2,  3,  4,  6,   9,  13, ... = A000930
  1, 1, 1, 1,  2,  3,  4,   5,   7, ... = A003269
  ... with the next rows A003520, A005708, A005709, ... such that beginning with the Fibonacci row, the succession of rows are recursive sequences generated from a(n) = a(n-1) + a(n-2); a(n) = a(n-1) + a(n-3), ... a(n) = a(n-1) + a(n-k); k = 2,3,4,... Last, columns going up from the topmost 1 become rows of triangle A141539. (End)

			A(4,2) = 6, because 6 binary words of length 4 have at least 2 "0" between any two "1" digits: 0000, 0001, 0010, 0100, 1000, 1001.
Square array A(n,k) begins:
    1,  1,  1,  1,  1,  1,  1,  1, ...
    2,  2,  2,  2,  2,  2,  2,  2, ...
    4,  3,  3,  3,  3,  3,  3,  3, ...
    8,  5,  4,  4,  4,  4,  4,  4, ...
   16,  8,  6,  5,  5,  5,  5,  5, ...
   32, 13,  9,  7,  6,  6,  6,  6, ...
   64, 21, 13, 10,  8,  7,  7,  7, ...
  128, 34, 19, 14, 11,  9,  8,  8, ...

Alois P. Heinz, Table of n, a(n) for n = 0..140, flattened

Cf. column k=0: A000079, k=1: A000045(n+2), k=2: A000930(n+2), A068921, A078012(n+5), k=3: A003269(n+4), A017898(n+7), k=4: A003520(n+4), A017899(n+9), k=5: A005708(n+5), A017900(n+11), k=6: A005709(n+6), A017901(n+13), k=7: A005710(n+7), A017902(n+15), k=8: A005711(n+7), A017903(n+17), k=9: A017904(n+19), k=10: A017905(n+21), k=11: A017906(n+23), k=12: A017907(n+25), k=13: A017908(n+27), k=14: A017909(n+29).
Main diagonal gives A000027(n+1).
A(2n,n) gives A000217(n+1)
A(3n,n) gives A008778.
A(3n,2n) gives A034856(n+1).
A(2n,3n) gives A005408.
A(2^n-1,n) gives A376697.
See also A143291.

A:= proc(n, k) option remember;
      if k=0 then 2^n
    elif n<=k and n>=0 then n+1
    elif n>0 then A(n-1, k) +A(n-k-1, k)
    else          A(n+1+k, k) -A(n+k, k)
      fi
    end:
seq(seq(A(n, d-n), n=0..d), d=0..15);

a[n_, k_] := a[n, k] = Which[k == 0, 2^n, n <= k && n >= 0, n+1, n > 0, a[n-1, k] + a[n-k-1, k], True, a[n+1+k, k] - a[n+k, k]]; Table[Table[a[n, d-n], {n, 0, d}], {d, 0, 15}] // Flatten (* Jean-François Alcover, Dec 17 2013, translated from Maple *)

G.f. of column k: x^(-k)/(1-x-x^(k+1)).

A(n,k) = 2^n if k=0, otherwise A(n,k) = n+1 if n<=k, otherwise A(n,k) = A(n-1,k) + A(n-k-1,k).

A017902 Expansion of 1/(1 - x^8 - x^9 - ...).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 119, 148, 184, 228, 281, 345, 423, 519, 638, 786, 970, 1198, 1479, 1824, 2247, 2766, 3404, 4190, 5160, 6358, 7837, 9661, 11908, 14674, 18078

Offset: 0

N. J. A. Sloane

A Lamé sequence of higher order.
a(n) = number of compositions of n in which each part is >=8. - Milan Janjic, Jun 28 2010
a(n+8) equals the number of n-length binary words such that 0 appears only in a run which length is a multiple of 8. - Milan Janjic, Feb 17 2015

Alois P. Heinz, Table of n, a(n) for n = 0..1000
I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5
J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380.
Augustine O. Munagi, Integer Compositions and Higher-Order Conjugation, J. Int. Seq., Vol. 21 (2018), Article 18.8.5.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 1).

For Lamé sequences of orders 1 through 9 see A000045, A000930, A017898-A017904.

f := proc(r) local t1,i; t1 := []; for i from 1 to r do t1 := [op(t1),0]; od: for i from 1 to r+1 do t1 := [op(t1),1]; od: for i from 2*r+2 to 50 do t1 := [op(t1),t1[i-1]+t1[i-1-r]]; od: t1; end; # set r = order
a:= n-> (Matrix(8, (i,j)-> if (i=j-1) then 1 elif j=1 then [1, 0$6, 1][i] else 0 fi)^n)[8,8]: seq(a(n), n=0..53); # Alois P. Heinz, Aug 04 2008

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0}, 60] (* Jean-François Alcover, Feb 13 2016 *)

a(n)=([0,1,0,0,0,0,0,0; 0,0,1,0,0,0,0,0; 0,0,0,1,0,0,0,0; 0,0,0,0,1,0,0,0; 0,0,0,0,0,1,0,0; 0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,1; 1,0,0,0,0,0,0,1]^n*[1;0;0;0;0;0;0;0])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

G.f.: (x-1)/(x-1+x^8). - Alois P. Heinz, Aug 04 2008
For positive integers n and k such that k <= n <= 8*k, and 7 divides n-k, define c(n,k) = binomial(k,(n-k)/7), and c(n,k) = 0, otherwise. Then, for n>=1, a(n+8) = sum(c(n,k), k=1..n). - Milan Janjic, Dec 09 2011
a(n) = A005710(n)-A005710(n-1). - R. J. Mathar, Sep 07 2016

A246690 Number A(n,k) of compositions of n into parts of the k-th list of distinct parts in the order given by A246688; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 3, 1, 1, 0, 1, 0, 1, 1, 5, 0, 1, 0, 1, 1, 0, 2, 0, 8, 1, 1, 0, 1, 0, 1, 0, 3, 0, 13, 0, 1, 0, 1, 0, 1, 1, 1, 4, 1, 21, 1, 1, 0, 1, 1, 0, 1, 2, 0, 6, 0, 34, 0, 1, 0, 1, 1, 2, 0, 1, 3, 0, 9, 0, 55, 1, 1, 0

Offset: 0

Alois P. Heinz, Sep 01 2014

The first lists of distinct parts in the order given by A246688 are: 0:[], 1:[1], 2:[2], 3:[1,2], 4:[3], 5:[1,3], 6:[4], 7:[1,4], 8:[2,3], 9:[5], 10:[1,2,3], 11:[1,5], 12:[2,4], 13:[6], 14:[1,2,4], 15:[1,6], 16:[2,5], 17:[3,4], 18:[7], 19:[1,2,5], 20:[1,3,4], ... .

			Square array A(n,k) begins:
  1, 1, 1,  1, 1,  1, 1,  1, 1, 1,   1, 1, 1, 1,   1, ...
  0, 1, 0,  1, 0,  1, 0,  1, 0, 0,   1, 1, 0, 0,   1, ...
  0, 1, 1,  2, 0,  1, 0,  1, 1, 0,   2, 1, 1, 0,   2, ...
  0, 1, 0,  3, 1,  2, 0,  1, 1, 0,   4, 1, 0, 0,   3, ...
  0, 1, 1,  5, 0,  3, 1,  2, 1, 0,   7, 1, 2, 0,   6, ...
  0, 1, 0,  8, 0,  4, 0,  3, 2, 1,  13, 2, 0, 0,  10, ...
  0, 1, 1, 13, 1,  6, 0,  4, 2, 0,  24, 3, 3, 1,  18, ...
  0, 1, 0, 21, 0,  9, 0,  5, 3, 0,  44, 4, 0, 0,  31, ...
  0, 1, 1, 34, 0, 13, 1,  7, 4, 0,  81, 5, 5, 0,  55, ...
  0, 1, 0, 55, 1, 19, 0, 10, 5, 0, 149, 6, 0, 0,  96, ...
  0, 1, 1, 89, 0, 28, 0, 14, 7, 1, 274, 8, 8, 0, 169, ...

Alois P. Heinz, Antidiagonals n = 0..140

Columns k=0-21, 23, 25-28 give: A000007, A000012, A059841, A000045(n+1), A079978, A000930, A121262, A003269(n+1), A182097, A079998, A000073(n+2), A003520, A079977, A079979, A060945, A005708, A001687(n+1), A017817, A082784, A079971, A006498, A005709, A052920, A120400, A060961, A005710, A013979.
Main diagonal gives A246691.
Cf. A246688, A246720 (the same for partitions).

b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i>n, [],
      [map(x->[i, x[]], b(n-i, i+1))[], b(n, i+1)[]]))
    end:
f:= proc() local i, l; i, l:=0, [];
      proc(n) while n>=nops(l)
        do l:=[l[], b(i, 1)[]]; i:=i+1 od; l[n+1]
      end
    end():
g:= proc(n, l) option remember; `if`(n=0, 1,
      add(`if`(i>n, 0, g(n-i, l)), i=l))
    end:
A:= (n, k)-> g(n, f(k)):
seq(seq(A(n, d-n), n=0..d), d=0..14);

b[n_, i_] := b[n, i] = If[n == 0, {{}}, If[i>n, {}, Join[Prepend[#, i]& /@ b[n - i, i + 1], b[n, i + 1]]]];
f = Module[{i = 0, l = {}}, Function[n, While[n >= Length[l], l = Join[l, b[i, 1]]; i++]; l[[n + 1]]]];
g[n_, l_] := g[n, l] = If[n==0, 1, Sum[If[i>n, 0, g[n - i, l]], {i, l}]];
A[n_, k_] := g[n, f[k]];
Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

A367800 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^8)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 119, 148, 184, 228, 281, 345, 423, 519, 638, 786, 970, 1198, 1479, 1824, 2247, 2766, 3404, 4190, 5160, 6358, 7837, 9661, 11908, 14674, 18078, 22268, 27428, 33786, 41623

Offset: 0

Seiichi Manyama, Dec 01 2023

nonn

a(n) = A005710(n-1) up to n=72, but then the two sequences start to differ. - R. J. Mathar, Dec 04 2023

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000621, A367794, A367637.

Cf. A005710, A101918.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\8, v[j+1]*v[i-8*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/8)} a(k) * a(n-1-8*k).

A143286 Number of binary words of length n containing at least one subword 10^{6}1 and no subwords 10^{i}1 with i<6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 9, 13, 19, 27, 37, 49, 63, 80, 102, 132, 173, 228, 300, 392, 508, 654, 839, 1076, 1382, 1778, 2289, 2945, 3783, 4850, 6207, 7934, 10135, 12943, 16526, 21095, 26915, 34320, 43733, 55692, 70882, 90174, 114673, 145778

Offset: 0

Alois P. Heinz, Aug 04 2008

			a(9)=2 because 2 binary words of length 9 have at least one subword 10^{6}1 and no subwords 10^{i}1 with i<6: 010000001, 100000010.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,1,0,-1,0,0,0,0,0,-1).

Cf. A005709, A005710, 6th column of A143291.

[n le 8 select 0 else n le 15 select n-8 else 2*Self(n-1)-Self(n-2) +Self(n-7)-Self(n-9)-Self(n-15): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013

a:= n-> coeff(series(x^8/((x^7+x-1)*(x^8+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);

CoefficientList[Series[x^8 / ((x^7 + x - 1) (x^8 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 04 2013 *)

G.f.: x^8/((x^7+x-1)*(x^8+x-1)).
a(n) = A005709(n+6)-A005710(n+7).
a(n) = 2*a(n-1) - a(n-2) + a(n-7) - a(n-9) - a(n-15). - Vincenzo Librandi, Jun 05 2013

A143287 Number of binary words of length n containing at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 14, 20, 28, 38, 50, 64, 80, 99, 123, 155, 198, 255, 329, 423, 540, 684, 861, 1080, 1354, 1700, 2139, 2696, 3400, 4285, 5392, 6772, 8490, 10630, 13300, 16637, 20812, 26036, 32568, 40726, 50902, 63582, 79372

Offset: 0

Alois P. Heinz, Aug 04 2008

			a(10)=2 because 2 binary words of length 10 have at least one subword 10^{7}1 and no subwords 10^{i}1 with i<7: 0100000001, 1000000010.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1).

Cf. A005710, A005711, 7th column of A143291.

[n le 9 select 0 else n le 17 select n-9 else 2*Self(n-1)-Self(n-2) +Self(n-8)-Self(n-10)-Self(n-17): n in [1..60]]; // Vincenzo Librandi, Jun 05 2013

a:= n-> coeff(series(x^9/((x^8+x-1)*(x^9+x-1)), x, n+1), x, n):
seq(a(n), n=0..60);

CoefficientList[Series[x^9 / ((x^8 + x - 1) (x^9 + x - 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 04 2013 *)

G.f.: x^9/((x^8+x-1)*(x^9+x-1)).
a(n) = A005710(n+7)-A005711(n+7).
a(n) = 2*a(n-1) - a(n-2) + a(n-8) - a(n-10) - a(n-17). - Vincenzo Librandi, Jun 05 2013

cp's OEIS Frontend

A058364 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 9 sites wide.

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Formula

A058365 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 8 sites wide.

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Formula

A058366 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 7 sites wide.

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Formula

A058367 Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 6 sites wide.

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Formula

A141539 Square array A(n,k) of numbers of length n binary words with at least k "0" between any two "1" digits (n,k >= 0), read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A017902 Expansion of 1/(1 - x^8 - x^9 - ...).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A246690 Number A(n,k) of compositions of n into parts of the k-th list of distinct parts in the order given by A246688; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

A367800 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^8)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs