A080014 -id:A080014 - cp's OEIS frontend

A079992 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,2}.

1, 1, 2, 3, 9, 19, 49, 100, 233, 503, 1166, 2580, 5884, 13092, 29622, 66281, 149569, 335524, 755737, 1697149, 3819301, 8582469, 19306314, 43397191, 97600441, 219421360, 493425528, 1109386496, 2494606984, 5608933040, 12612101201

Offset: 0

Vladimir Baltic, Feb 17 2003

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, 3, -1, 1, 1, 3, -5, -9, 1, 1, 1, -1, 1, 1).

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

a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) +a(n-5) +3*a(n-6) -5*a(n-7) -9*a(n-8) +a(n-9) +a(n-10) +a(n-11) -a(n-12) +a(n-13) +a(n-14).

G.f.: -(x^2-1)*(x^6+x^4+x^3+x^2-1)/(x^14 +x^13 -x^12 +x^11 +x^10 +x^9 -9*x^8 -5*x^7 +3*x^6 +x^5 +x^4 -x^3 +3*x^2 +x-1)

A079993 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={0,2}.

Original entry on oeis.org

1, 0, 1, 1, 5, 9, 23, 39, 97, 197, 465, 969, 2161, 4605, 10202, 22051, 48438, 105028, 229692, 499620, 1091268, 2376641, 5185742, 11299467, 24645179, 53718931, 117144203, 255371099, 556824105, 1213941393, 2646824821, 5770590379

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,0}.

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, 2, 2, 4, 6, 11, 1, -6, -4, -4, -8, -10, 1, 7, 0, -2, 0, 2, 0, -1).

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

a(n) = 2*a(n-2) +2*a(n-3) +4*a(n-4) +6*a(n-5) +11*a(n-6) +a(n-7) -6*a(n-8) -4*a(n-9) -4*a(n-10) -8*a(n-11) -10*a(n-12) +a(n-13) +7*a(n-14) -2*a(n-16) +2*a(n-18) -a(n-20).

G.f.: -(x^3+1)*(x^11-x^9-2*x^8-x^7+2*x^6+x^4+2*x^3+x^2-1)/((x^18 -x^17 -2*x^16 +3*x^15 +x^14 -4*x^13 -4*x^12 +7*x^11 +7*x^10 -6*x^9 +3*x^8 +7*x^7 -4*x^6 -4*x^5 -3*x^4 +x^3 -2*x^2 -x+1) *(x^2+x+1)).

A079994 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={0,1}.

Original entry on oeis.org

1, 0, 0, 1, 3, 9, 13, 25, 59, 147, 328, 690, 1478, 3285, 7357, 16249, 35561, 77974, 171891, 379401, 835954, 1839288, 4047688, 8914186, 19636159, 43244340, 95216488, 209653186, 461673635, 1016681969, 2238835524, 4929989552

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

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

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, 2, 2, 4, 9, 10, -3, -9, 0, -1, -12, -11, 1, 4, -1, 0, 0, 2, 0, -1).

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

a(n) = 2*a(n-2) +2*a(n-3) +4*a(n-4) +9*a(n-5) +10*a(n-6) -3*a(n-7) -9*a(n-8) -a(n-10) -12*a(n-11) -11*a(n-12) +a(n-13) +4*a(n-14) -a(n-15) +2*a(n-18) -a(n-20).

G.f.: -(x^14 -2*x^12 -x^11 -x^10 +2*x^9 -3*x^8 +5*x^6 +2*x^5 +x^4 +x^3 +2*x^2 -1)/ (x^20 -2*x^18 +x^15 -4*x^14 -x^13 +11*x^12 +12*x^11 +x^10 +9*x^8 +3*x^7 -10*x^6 -9*x^5 -4*x^4 -2*x^3 -2*x^2+1)

A079996 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={1}.

Original entry on oeis.org

1, 1, 1, 3, 11, 33, 82, 198, 516, 1389, 3690, 9642, 25143, 65867, 173092, 454578, 1192227, 3125940, 8198836, 21509532, 56429115, 148023671, 388279519, 1018515853, 2671777153, 7008626377, 18384947908, 48227023198, 126508325008

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-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.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (1, 2, 3, 4, 9, 9, -15, -12, 0, 7, -6, -6, 5, 5, 3, -2, -1, 2, -1, -1).

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

a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +4*a(n-4) +9*a(n-5) +9*a(n-6) -15*a(n-7) -12*a(n-8) +7*a(n-10) -6*a(n-11) -6*a(n-12) +5*a(n-13) +5*a(n-14) +3*a(n-15) -2*a(n-16) -a(n-17) +2*a(n-18) -a(n-19) -a(n-20).

G.f.: -(x^14 -2*x^12 +x^11 -x^10 -2*x^8 -2*x^7 +4*x^6 +x^4 +3*x^3 +2*x^2-1) /(x^20 +x^19 -2*x^18 +x^17 +2*x^16 -3*x^15 -5*x^14 -5*x^13 +6*x^12 +6*x^11 -7*x^10 +12*x^8 +15*x^7 -9*x^6 -9*x^5 -4*x^4 -3*x^3 -2*x^2 -x+1)

A079999 Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,-1,3} for all i=1,...,n.

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 1, 1, 1, 4, 4, 5, 7, 10, 16, 22, 29, 40, 60, 84, 118, 165, 230, 330, 466, 653, 919, 1297, 1831, 2585, 3640, 5124, 7233, 10201, 14380, 20272, 28572, 40289, 56816, 80096, 112912, 159196, 224449, 316456, 446164, 629004, 886821, 1250329, 1762801

Offset: 0

Vladimir Baltic, Feb 10 2003

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 A. Allen and Kenneth Edwards, Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices, Linear and Multilinear Algebra, 72:13 (2024), 2091-2103.
Michael A. Allen and Kenneth Edwards, Identities relating permanents of some classes of (0,1) Toeplitz matrices to generalized Fibonacci numbers, Fibonacci Quarterly, 63:2 (2025), 163-177.
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 (0,0,1,1,2,1,0,-1,0,-1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A376743.

LinearRecurrence[{0,0,1,1,2,1,0,-1,0,-1},{1,0,0,0,1,1,1,1,1,4},50] (* Harvey P. Dale, Dec 12 2024 *)

Recurrence: a(n) = a(n-3) + a(n-4) + 2*a(n-5) + a(n-6) - a(n-8) - a(n-10) for n>=10.

G.f.: (1 - x^3 - x^5)/(1 - x^3 - x^4 - 2*x^5 - x^6 + x^8 + x^10).

A080001 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={-1,0,2}.

Original entry on oeis.org

1, 0, 0, 1, 1, 1, 1, 2, 4, 3, 4, 8, 10, 13, 16, 24, 36, 43, 59, 85, 115, 156, 207, 289, 401, 533, 729, 1002, 1368, 1864, 2526, 3465, 4740, 6436, 8785, 11995, 16375, 22331, 30420, 41550, 56705, 77296, 105456, 143874, 196321, 267792, 365216, 498356

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

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 (0, 0, 1, 1, 2, 0, 0, 0, -1, -1).

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

Recurrence: a(n) = a(n-3)+a(n-4)+2*a(n-5)-a(n-9)-a(n-10) G.f.: -(x^5-1)/(x^10+x^9-2*x^5-x^4-x^3+1)

A080002 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={-1,0,1}.

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 0, 0, 1, 3, 1, 1, 1, 6, 6, 4, 5, 10, 20, 16, 20, 25, 50, 60, 66, 85, 125, 190, 216, 281, 365, 545, 701, 883, 1156, 1576, 2176, 2761, 3636, 4784, 6560, 8620, 11265, 14856, 19840, 26600, 34825, 46045, 60856, 81420, 107625, 142055, 187881, 249461

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

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 (0,1,0,1,2,-1,-1,0,0,-1).

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

LinearRecurrence[{0,1,0,1,2,-1,-1,0,0,-1},{1,0,0,0,1,1,0,0,1,3},60] (* Harvey P. Dale, Dec 14 2011 *)

Recurrence: a(n) = a(n-2)+a(n-4)+2*a(n-5)-a(n-6)-a(n-7)-a(n-10).

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

A080003 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={1,2}.

Original entry on oeis.org

1, 1, 1, 1, 4, 8, 13, 22, 40, 77, 140, 252, 456, 834, 1525, 2775, 5049, 9195, 16760, 30536, 55617, 101304, 184544, 336193, 612424, 1115600, 2032216, 3702000, 6743761, 12284729, 22378393, 40765513, 74260396, 135276192, 246425309

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

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 (1,0,1,2,2,0,1,-1,0,-1).

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

Recurrence: a(n) = a(n-1)+a(n-3)+2*a(n-4)+2*a(n-5)+a(n-7)-a(n-8)-a(n-10).

G.f.: -(x^5+x^3-1)/(x^10+x^8-x^7-2*x^5-2*x^4-x^3-x+1)

A080004 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={-1,2}.

Original entry on oeis.org

1, 1, 1, 2, 4, 9, 15, 25, 46, 84, 156, 280, 501, 909, 1647, 2990, 5408, 9773, 17695, 32033, 58000, 104976, 189968, 343860, 622409, 1126617, 2039201, 3690898, 6680644, 12092173, 21887215, 39616409, 71706406, 129790404, 234923948

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

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
K. Edwards and M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, Volume 187, 31 May 2015, Pages 82-90.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,4,-1,1,0,-1,-1).

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

LinearRecurrence[{1,0,1,1,4,-1,1,0,-1,-1},{1,1,1,2,4,9,15,25,46,84},40] (* Harvey P. Dale, Jun 18 2013 *)

a(n) = a(n-1)+a(n-3)+a(n-4)+4*a(n-5)-a(n-6)+a(n-7)-a(n-9)-a(n-10).

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

A080005 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}.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 11, 19, 35, 62, 107, 186, 328, 578, 1012, 1771, 3107, 5455, 9568, 16774, 29417, 51603, 90513, 158741, 278404, 488301, 856448, 1502116, 2634532, 4620700, 8104269, 14214069, 24929981, 43724610, 76688540, 134503903, 235906039

Offset: 0

Vladimir Baltic, Feb 10 2003

nonn

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.
K. Edwards, M. A. Allen, Strongly restricted permutations and tiling with fences, Discrete Applied Mathematics, Volume 187, 31 May 2015, Pages 82-90.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,1,-2,0,1,0,-1).

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

CoefficientList[Series[-(x^5 + x^2 - 1)/(x^10 - x^8 + 2*x^6 - x^5 - x^4 - x^2 - x + 1), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jan 02 2017 *)

a(n) = a(n-1) + a(n-2) + a(n-4) + a(n-5) - 2*a(n-6) + a(n-8) - a(n-10), n>9.

G.f.: -(x^5+x^2-1)/(x^10-x^8+2*x^6-x^5-x^4-x^2-x+1).

cp's OEIS Frontend

A079992 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,2}.

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A079993 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={0,2}.

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A079994 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={0,1}.

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A079996 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={1}.

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A079999 Number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) such that p(i)-i is in {-2,-1,3} for all i=1,...,n.

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A080001 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={-1,0,2}.

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A080002 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={-1,0,1}.

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A080003 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={1,2}.

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A080004 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={-1,2}.

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