A002524 -id:A002524 - cp's OEIS frontend

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

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).

A154659 Number of permutations of length n within distance 10.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 402796800, 3770686080, 33187593600, 278598101040, 2261952938160, 17986137205800, 141564484858104, 1112444773251726, 8787513806478134, 70146437009397871, 568128719132038153, 4647312969412825372

Offset: 0

Torleiv Kløve, Jan 13 2009

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..100
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.

Cf. A000045, A002524, A002526, A072856, A154654-A154658.

Column k=10 of A306209.

More terms from Alois P. Heinz, Jan 13 2014

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))

A376743 Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,-1,4} for all i=1,...,n.

Original entry on oeis.org

1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 5, 5, 6, 8, 11, 15, 25, 35, 46, 61, 85, 125, 175, 245, 341, 470, 650, 925, 1300, 1810, 2521, 3520, 4915, 6880, 9640, 13476, 18801, 26251, 36721, 51346, 71776, 100335, 140210, 195886, 273813, 382821, 535105, 747850, 1045220

Offset: 0

Michael A. Allen, Oct 03 2024

Other sequences related to strongly restricted permutations pi(i) of i in {1,..,n} along with the sets of allowed p(i)-i (containing at least 3 elements): A000045 {-1,0,1}, A189593 {-1,0,2,3,4,5,6}, A189600 {-1,0,2,3,4,5,6,7}, A006498 {-2,0,2}, A080013 {-2,1,2}, A080014 {-2,0,1,2}, A033305 {-2,-1,1,2}, A002524 {-2,-1,0,1,2}, A080000 {-2,0,3}, A080001 {-2,1,3}, A080004 {-2,0,1,3}, A080002 {-2,2,3}, A080005 {-2,0,2,3}, A080008 {-2,1,2,3}, A080011 {-2,0,1,2,3}, A079999 {-2,-1,3}, A080003 {-2,-1,0,3}, A080006 {-2,-1,1,3}, A080009 {-2,-1,0,1,3}, A080007 {-2,-1,2,3}, A080010 {-2,-1,0,2,3}, A080012 {-2,-1,1,2,3}, A072827 {-2,-1,0,1,2,3}, A224809 {-2,0,4}, A189585 {-2,0,1,3,4}, A189581 {-2,-1,0,3,4}, A072850 {-2,-1,0,1,2,3,4}, A189587 {-2,0,1,3,4,5}, A189588 {-2,-1,0,3,4,5}, A189594 {-2,0,1,3,4,5,6}, A189595 {-2,-1,0,3,4,5,6}, A189601 {-2,0,1,3,4,5,6,7}, A189602 {-2,-1,0,3,4,5,6,7}, A224811 {-2,0,8}, A224812 {-2,0,10}, A224813 {-2,0,12}, A006500 {-3,0,3}, A079981 {-3,1,3}, A079983 {-3,0,1,3}, A079982 {-3,2,3}, A079984 {-3,0,2,3}, A079988 {-3,1,2,3}, A079989 {-3,0,1,2,3}, A079986 {-3,-1,1,3}, A079992 {-3,-1,0,1,3}, A079987 {-3,-1,2,3}, A079990 {-3,-1,0,2,3}, A079993 {-3,-1,1,2,3}, A079985 {-3,-2,2,3}, A079991 {-3,-2,0,2,3}, A079996 {-3,-2,0,1,2,3}, A079994 {-3,-2,1,2,3}, A079997 {-3,-2, -1,1,2,3}, A002526 {-3,-2,-1,0,1,2,3}, A189586 {-3,0,1,2,4}, A189583 {-3,-1,0,2,4}, A189582 {-3,-2,0,1,4}, A189584 {-3,-2,-1,0,4}, A189589 {-3,0,1,2,4,5}, A189590 {-3,-1,0,2,4,5}, A189591 {-3,-2,1,4,5}, A189592 {-3,-2,-1,0,4,5}, A224810 {-3,0,6}, A189596 {-3,0,1,2,4,5,6}, A189597 {-3,-1,0,2,4,5,6}, A189598 {-3,-2,0,1,4,5,6}, A189599 {-3,-2,-1,0,4,5,6}, A224814 {-3,0,9}, A031923 {-4,0,4}, A072856 {-4,-3, -2,-1,0,1,2,3,4}, A224815 {-4,0,8}, A154654 {-5,-4,-3,-2,-1,0,1,2,3,4,5}, A154655 {-6,-5,-4,-3, -2,-1,0,1,2,3,4,5,6}.

[Keyword "less", because this comment should be moved to the Index to the OEIS, it is not appropriate here. - N. J. A. Sloane, Oct 25 2024]

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

Michael A. Allen and Kenneth Edwards, Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices, Lin. Multilin. Alg. 72:13 (2024) 2091-2103.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics, 4(1) (2010), 119-135.
Kenneth Edwards and Michael A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, 187 (2015), 82-90.
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,1,2,1,0,-2,-2,0,-1,0,0,1).

See comments for other sequences related to strongly restricted permutations.

CoefficientList[Series[(1 - x^3 - x^4 - x^6 + x^9)/(1 - x^3 - x^4 - x^5 - 2*x^6 - x^7 + 2*x^9 + 2*x^10 + x^12 - x^15),{x,0,49}],x]
LinearRecurrence[{0, 0, 1, 1, 1, 2, 1, 0, -2, -2, 0, -1, 0, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 5, 5, 6, 8}, 50]

a(n) = a(n-3) + a(n-4) + a(n-5) + 2*a(n-6) + a(n-7) - 2*a(n-9) - 2*a(n-10) - a(n-12) + a(n-15).

G.f.: (1 - x^3 - x^4 - x^6 + x^9)/(1 - x^3 - x^4 - x^5 - 2*x^6 - x^7 + 2*x^9 + 2*x^10 + x^12 - x^15).

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

A080000 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={-1,1,2}.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 5, 7, 9, 12, 16, 24, 35, 50, 70, 96, 135, 190, 270, 383, 539, 759, 1065, 1500, 2116, 2985, 4212, 5932, 8356, 11770, 16585, 23381, 32953, 46445, 65445, 92216, 129951, 183129, 258091, 363719, 512566, 722316, 1017886, 1434445, 2021476

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

			G.f. = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 7*x^8 + 9*x^9 + ...
a(5) = 2 for permutations [1,2,3,4,5] and [4,5,1,2,3].

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 (April, 2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 2, -1, 1, 0, 0, -1).

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

G.f.: -(x^5-1)/(x^10-x^7+x^6-2*x^5-x+1).

a(n) = a(n-1)+2*a(n-5)-a(n-6)+a(n-7)-a(n-10).

cp's OEIS Frontend

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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A154659 Number of permutations of length n within distance 10.

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

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PARI

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A376743 Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,-1,4} for all i=1,...,n.

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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}.

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