A002529 -id:A002529 - cp's OEIS frontend

A080013 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={0,1}.

1, 0, 0, 1, 1, 1, 1, 3, 3, 4, 6, 9, 12, 16, 24, 33, 46, 64, 91, 127, 177, 249, 349, 489, 684, 960, 1345, 1884, 2640, 3700, 5185, 7264, 10180, 14265, 19989, 28009, 39249, 54999, 77067, 107992, 151326, 212049, 297136, 416368, 583444, 817561, 1145622, 1605324, 2249491, 3152139, 4416993

Offset: 0

Vladimir Baltic, Jan 24 2003

nonn

Also the number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={0,-1}.

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Michael De Vlieger, Table of n, a(n) for n = 0..6829
Michael A. Allen and Kenneth Edwards, Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices, arXiv:2107.02589 [math.CO], 2021.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Tomislav Došlić, Mate Puljiz, Stjepan Šebek, and Josip Žubrinić, On a variant of Flory model, arXiv:2210.12411 [math.CO], 2022.
P. L. Krapivsky and J. M. Luck, Jamming and metastability in one dimension: from the kinetically constrained Ising chain to the Riviera model, arXiv:2211.12815 [cond-mat.stat-mech], 2022.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,0,-1).

Cf. A002524..A002529, A072827, A072850..A072856, A079955..A080014.

LinearRecurrence[{0,1,1,1,0,-1},{1,0,0,1,1,1},60] (* Harvey P. Dale, Aug 08 2019 *)

Recurrence: a(n) = a(n-2)+a(n-3)+a(n-4)-a(n-6).

G.f.: -(x^2-1)/(x^6-x^4-x^3-x^2+1)

A224811 Number of subsets of {1,2,...,n-8} without differences equal to 2, 4, 6 or 8.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 48, 64, 88, 121, 165, 225, 300, 400, 520, 676, 884, 1156, 1530, 2025, 2700, 3600, 4800, 6400, 8480, 11236, 14840, 19600, 25900, 34225, 45325, 60025, 79625, 105625, 140075, 185761, 246101, 326041, 431676, 571536, 756756, 1002001, 1327326, 1758276, 2329782, 3087049, 4090296, 5419584

Offset: 0

Vladimir Baltic, May 18 2013

nonn

Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i in the set I, i=1..n, with k=2, r=8, I={-2,0,8}.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael A. Allen, On a Two-Parameter Family of Generalizations of Pascal's Triangle, arXiv:2209.01377 [math.CO], 2022.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, -1, 1, -1, 1, 2, -1, 1, 0, 0, -2, 1, -2, 0, 0, -1, 0, 0, 0, 0, 1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694,A224808-A224810.

CoefficientList[Series[(1 - x^10 - x^5 - x^7 + x^15)/((1 - x)*(1 + x)*(x^2 - x + 1)*(x^3 + x^2 - 1)*(x^6 - x^2 - 1)*(x^12 + x^10 + x^8 + 2*x^6 + x^4 + 1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 28 2017 *)

x='x+O('x^50); Vec((1-x^10-x^5-x^7+x^15)/((1-x)*(1+x)*(x^2-x+1)*( x^3+x^2-1)*(x^6-x^2-1)*(x^12+x^10+x^8+2*x^6+x^4+1) )) \\ G. C. Greubel, Oct 28 2017

a(n) = a(n-1) +a(n-5) -a(n-6) +a(n-7) -a(n-8) +a(n-9) +2*a(n-10) -a(n-11) +a(n-12) -2*a(n-15) +a(n-16) -2*a(n-17) -a(n-20) +a(n-25).
G.f.: (1-x^10-x^5-x^7+x^15) / ( (1-x) *(1+x) *(x^2-x+1) *(x^3+x^2-1) *(x^6-x^2-1) *(x^12+x^10+x^8+2*x^6+x^4+1) ).
a(2*k) = (A003520(k))^2,
a(2*k+1) = A003520(k) * A003520(k+1)

A224815 Number of subsets of {1,2,...,n-8} without differences equal to 4 or 8.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 24, 36, 54, 81, 108, 144, 192, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561, 9477, 13689, 19773, 28561, 41743, 61009, 89167, 130321, 192052, 283024, 417088, 614656, 900032, 1317904, 1929788, 2825761

Offset: 0

Vladimir Baltic, May 18 2013

a(n) is the number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i in the set I, i=1..n, with k=4, r=8, I={-4,0,8}.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-13
Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, -2, 2, 0, 2, -6, 6, 0, 6, 1, -1, 0, -1, 13, -13, 0, -13, 15, -15, 0, -15, -6, 6, 0, 6, 3, -3, 0, -3, -2, 2, 0, 2, 8, -8, 0, -8, 3, -3, 0, -3, -1, 1, 0, 1, -1, 1, 0, 1).

Cf. A000930, A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808-A224814.

CoefficientList[Series[(1 - x^3 + x^4 - x^5 - x^6 - 3*x^7 + 3*x^8 - 2*x^9 - x^10 - 5*x^11 - 3*x^12 - 2*x^13 + 3*x^15 - 3*x^16 - 3*x^18 + 3*x^19 - 3*x^20 + 3*x^21 + 3*x^23 + 6*x^24 - 3*x^25 - 2*x^26 - 4*x^27 - x^29 - x^30 - 2*x^31 - x^32 + x^33 + x^35 - x^36 + x^37 + x^39)/((1 - x - x^3)*(1 + x^4 + x^6)*(1 + x^4 - x^6)*(1 - x^4 - x^12)*(1 + x^4 + 6*x^8 - 3*x^12 + 2*x^20 + x^24)), {x, 0, 50}], x] (* G. C. Greubel, Apr 28 2017 *)

a(n) = a(n-1)+a(n-3)-2*a(n-4)+2*a(n-5)+2*a(n-7)-6*a(n-8)+6*a(n-9)+6*a(n-11) +a(n-12)-a(n-13)-a(n-15)+13*a(n-16)-13*a(n-17)-13*a(n-19)+15*a(n-20)-15*a(n-21)-15*a(n-23)-6*a(n-24)+6*a(n-25)+6*a(n-27)+3*a(n-28)-3*a(n-29)-3*a(n-31)-2*a(n-32)+2*a(n-33)+2*a(n-35)+8*a(n-36)-8*a(n-37)-8*a(n-39)+3*a(n-40)-3*a(n-41)-3*a(n-43)-a(n-44)+a(n-45)+a(n-47)-a(n-48)+a(n-49)+a(n-51).
G.f.: ( 1-x^3+x^4-x^5-x^6-3*x^7+3*x^8-2*x^9-x^10-5*x^11-3*x^12-2*x^13 +3*x^15-3*x^16-3*x^18+3*x^19-3*x^20+3*x^21+3*x^23+6*x^24-3*x^25-2*x^26-4*x^27-x^29-x^30-2*x^31-x^32+x^33+x^35-x^36+x^37+x^39 ) / ((1-x-x^3)*(1+x^4+x^6)*(1+x^4-x^6)*(1-x^4-x^12)*(1+x^4+6*x^8-3*x^12+2*x^20+x^24)).
a(4*k) = (A000930(k))^4,
a(4*k+1) = (A000930(k))^3 * A000930(k+1),
a(4*k+2) = (A000930(k))^2 * (A000930(k+1))^2,
a(4*k+3) = A000930(k) * (A000930(k+1))^3.

A079957 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,3}.

Original entry on oeis.org

1, 0, 0, 1, 0, 1, 2, 0, 2, 3, 1, 5, 5, 3, 10, 9, 9, 20, 17, 22, 39, 35, 51, 76, 74, 112, 150, 160, 239, 300, 346, 501, 610, 745, 1040, 1256, 1592, 2151, 2611, 3377, 4447, 5459, 7120, 9209, 11447, 14944, 19115, 24026, 31273, 39771, 50417, 65332, 82912, 105716

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {3,5,6}.

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135.
Index entries for linear recurrences with constant coefficients, signature (0,0,1,0,1,1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

a(n) = a(n-3)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^3-1).

A079972 Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=4, I={1,2}.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 6, 8, 11, 17, 27, 41, 60, 88, 132, 200, 301, 449, 669, 1001, 1502, 2252, 3370, 5040, 7543, 11297, 16919, 25329, 37912, 56752, 84968, 127216, 190457, 285121, 426841, 639025, 956698, 1432276, 2144238, 3210104, 4805827, 7194801

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Number of compositions (ordered partitions) of n into elements of the set {1,4,5}.

a(n+3) is the number of length-n binary words with no substring 1x1 of 1xy1 (that is, no 1's occur with distance two or three), see fxtbook link. - Joerg Arndt, May 27 2011

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Michael De Vlieger, Table of n, a(n) for n = 0..5708
Michael A. Allen, Connections between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings, arXiv:2409.00624 [math.CO], 2024. See p. 18.
Said Amrouche and Hacène Belbachir, Unimodality and linear recurrences associated with rays in the Delannoy triangle, Turkish Journal of Mathematics (2019) Vol. 44, 118-130.
Joerg Arndt, Matters Computational (The Fxtbook), section 14.10.3, p. 322
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

CoefficientList[Series[1/(1 - x - x^4 - x^5), {x, 0, 41}], x] (* Michael De Vlieger, Feb 03 2020 *)

a(n):=sum(sum(binomial(k,j)*binomial(j,n-k-3*j),j,floor((n-k)/4),floor((n-k)/3)),k,0,n); /* Vladimir Kruchinin, May 26 2011 */

a(n) = a(n-1) + a(n-4) + a(n-5).
G.f.: 1/(1-x-x^4-x^5).
a(n) = Sum_{k=0..n} Sum_{j=floor((n-k)/4)..floor((n-k)/3)} binomial(k,j)*binomial(j,n-k-3*j). - Vladimir Kruchinin, May 26 2011

A079973 Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=4, I={0,3}.

Original entry on oeis.org

1, 0, 1, 1, 1, 3, 2, 5, 6, 8, 14, 16, 27, 36, 51, 77, 103, 155, 216, 309, 448, 628, 912, 1292, 1849, 2652, 3769, 5413, 7713, 11031, 15778, 22513, 32222, 46004, 65766, 94004, 134283, 191992, 274291, 392041, 560287, 800615, 1144320, 1635193, 2336976

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Number of compositions (ordered partitions) of n into elements of the set {2,3,5}.

For n>=2, a(n) is number of compositions of n-2 with elements from the set {1,2,3} such that no two odd numbers appear consecutively. - Armend Shabani, Mar 01 2017

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,1).

Row sums of A059484. - N. J. A. Sloane, Jun 02 2009

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

CoefficientList[Series[-1/(x^5 + x^3 + x^2 - 1), {x, 0, 44}], x] (* Michael De Vlieger, Mar 02 2017 *)

a(n) = a(n-2) + a(n-3) + a(n-5).

G.f.: -1/(x^5 + x^3 + x^2 - 1).

A188379 a(n) = A002526(n+1) - A002527(n+1).

Original entry on oeis.org

0, 0, 0, 6, 18, 46, 115, 374, 1204, 3752, 11300, 34324, 105124, 322989, 989692, 3028484, 9267328, 28374898, 86891022, 266058106, 814585879, 2494006074, 7636057864, 23380074400, 71584762200, 219176102664, 671066472872, 2054652945289

Offset: 0

N. J. A. Sloane, Apr 01 2011

nonn

For n >= 3, a(n) is the number of permutations p on the set [n] with the properties that abs(p(i)-i) <= 3 for all i and p(j) <= 2+j for j = 1,2,3.
For n >= 3, a(n) is also the permanent of the n X n matrix that has ones on its diagonal, ones on its three superdiagonals, ones on its three subdiagonals (with the exception of zeros in the (4,1),(5,2), and (6,3)-entries), and is zero elsewhere.
This is row 4 of Kløve's Table 3.

Torleiv Kløve, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.

with (LinearAlgebra):
A188379:= n-> `if` (n<=2, 0, Permanent (Matrix (n, (i, j)->
              `if` (abs(j-i)<4 and [i, j]<>[4, 1] and [i, j]<>[5, 2] and [i, j]<>[6, 3], 1, 0)))):
seq (A188379(n), n=0..20);

a[n_] := Permanent[Table[If[Abs[j - i] < 4 && {i, j} != {4, 1} && {i, j} != {5, 2} && {i, j} != {6, 3}, 1, 0], {i, 1, n}, {j, 1, n}]]; a[1] = 0; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 20}] (* Jean-François Alcover, Jan 07 2016, adapted from Maple *)
CoefficientList[Series[-(x^10 + 2 x^9 + 2 x^7 + 4 x^6 - 2 x^5 - 8 x^4 - 13 x^3 - 2 x^2 + 6 x+6) x^3 / (x^14 + 2 x^13 + 2 x^11 + 4 x^10 - 2 x^9 - 10 x^8 - 16 x^7 - 2 x^6 + 8 x^5 + 10 x^4 + 2 x^2 + 2 x - 1), {x, 0, 33}], x] (* Vincenzo Librandi, Jan 07 2016 *)

a(n) = A002529(n-1) + A188492(n-1) + A188493(n-1). - Nathaniel Johnston, Apr 08 2011

G.f.: -(x^10 +2*x^9 +2*x^7 +4*x^6 -2*x^5 -8*x^4 -13*x^3 -2*x^2 +6*x+6) * x^3 / (x^14 +2*x^13 +2*x^11 +4*x^10 -2*x^9 -10*x^8 -16*x^7 -2*x^6 +8*x^5 +10*x^4 +2*x^2 +2*x-1). - Alois P. Heinz, Apr 07 2011

Name and comments edited by Nathaniel Johnston, Apr 08 2011

A224810 Subsets of {1,2,...,n-6} without differences equal to 3 or 6.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 96, 144, 216, 324, 486, 729, 1053, 1521, 2197, 3211, 4693, 6859, 10108, 14896, 21952, 32144, 47068, 68921, 100860, 147600, 216000, 316800, 464640, 681472, 998976

Offset: 0

Vladimir Baltic, May 16 2013

Number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=3, r=6, I={-2,-1,1,2,3,4,5}.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 2, 0, -2, 4, 0, 2, 2, 0, 4, -2, 0, 2, -4, 0, -2, -2, 0, -1, -1, 0, -1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694,A224808.

CoefficientList[Series[(1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18)), {x, 0, 50}], x] (* G. C. Greubel, Apr 30 2017 *)

x='x+O('x^50); Vec((1 + x^3 - x^4 - x^5 + x^6 - 2*x^7 - x^8 - x^9 - 2*x^10 - x^12 - x^13 - x^15)/((1 - x)*(1 + x + x^2)*(1 - x - x^3)*(1 + 3*x^3 + 7*x^6 + 9*x^9 + 7*x^12 + 3*x^15 + x^18))) \\ G. C. Greubel, Apr 30 2017

a(3*k) = (A000930(k))^3.
a(3*k+1) = (A000930(k))^2 * A000930(k+1).
a(3*k+2) = A000930(k) * (A000930(k+1))^2.
a(n) = a(n-1) -a(n-3) +2*a(n-4) -2*a(n-6) +4*a(n-7) +2*a(n-9) +2*a(n-10) +4*a(n-12) -2*a(n-13) +2*a(n-15) -4*a(n-16) -2*a(n-18) -2*a(n-19) -a(n-21) -a(n-22) -a(n-24)
G.f.: (1+x^3-x^4-x^5+x^6-2*x^7-x^8-x^9-2*x^10-x^12-x^13-x^15) / ((1-x)*(1+x+x^2)*(1-x-x^3)*(1+3*x^3+7*x^6+9*x^9+7*x^12+3*x^15+x^18))

A079958 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={3,4}.

Original entry on oeis.org

1, 1, 2, 4, 7, 13, 25, 46, 86, 161, 300, 560, 1046, 1952, 3644, 6803, 12699, 23706, 44254, 82611, 154215, 287883, 537408, 1003212, 1872757, 3495988, 6526172, 12182800, 22742368, 42454552, 79252477, 147945385, 276178586, 515559248

Offset: 0

Vladimir Baltic, Feb 19 2003

nonn

Number of compositions (ordered partitions) of n into elements of the set {1,2,3,6}.

Number of compositions of n with 3 frozen; that is, the order of the summand 3 does not matter. - Gregory L. Simay, Oct 01 2018

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,0,1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

LinearRecurrence[{1,1,1,0,0,1},{1,1,2,4,7,13},40] (* Harvey P. Dale, Jun 21 2024 *)

x='x+O('x^50); Vec(1/(1-x-x^2-x^3-x^6)) \\ Altug Alkan, Oct 02 2018

a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-6).

G.f.: -1/(x^6+x^3+x^2+x-1)

A079971 Number of compositions (ordered partitions) of n into parts 1, 2, and 5.

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 128, 218, 372, 634, 1081, 1843, 3142, 5357, 9133, 15571, 26547, 45260, 77164, 131557, 224292, 382396, 651948, 1111508, 1895013, 3230813, 5508222, 9390983, 16010713, 27296709, 46538235, 79343166, 135272384

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Number of ways of ordered sequences of nickels, dimes and quarters that add to 5n cents.

Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=4, I={2,3}.

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
Index entries for sequences related to making change.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A073031.

a:= n-> (Matrix(5, (i,j)-> if i+1=j or j=1 and member(i,[1, 2, 5]) then 1 else 0 fi)^n)[1, 1]: seq(a(n), n=0..40); # Alois P. Heinz, Oct 07 2008

LinearRecurrence[{1, 1, 0, 0, 1}, {1, 1, 2, 3, 5}, 40] (* Jean-François Alcover, Nov 11 2015 *)

a(n):=sum(sum(binomial(j,n-5*k+4*j)*binomial(k,j),j,floor((5*k-n)/4),k),k,0,n); /* Vladimir Kruchinin, Dec 15 2011 */

Recurrence: a(n) = a(n-1)+a(n-2)+a(n-5).
G.f.: 1/(1-x-x^2-x^5).
a(n) = Sum_{k=0..n} Sum_{j=floor((5*k-n)/4)..k} C(j,n-5*k+4*j)*C(k,j). - Vladimir Kruchinin, Dec 15 2011
With offset 1, the INVERT transform of (1 + x + x^4). - Gary W. Adamson, Apr 01 2017

Entry revised by N. J. A. Sloane, Feb 23 2006

cp's OEIS Frontend

A080013 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={0,1}.

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Mathematica

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A224811 Number of subsets of {1,2,...,n-8} without differences equal to 2, 4, 6 or 8.

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PARI

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A224815 Number of subsets of {1,2,...,n-8} without differences equal to 4 or 8.

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A079957 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,3}.

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A079972 Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=4, I={1,2}.

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Maxima

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A079973 Number of permutations satisfying -k <= p(i) - i <= r and p(i) - i not in I, i=1..n, with k=1, r=4, I={0,3}.

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A188379 a(n) = A002526(n+1) - A002527(n+1).

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Maple

Mathematica

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A224810 Subsets of {1,2,...,n-6} without differences equal to 3 or 6.

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