A080014 -id:A080014 - cp's OEIS frontend

A079963 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={1,2}.

1, 1, 1, 1, 2, 4, 7, 10, 14, 21, 34, 55, 86, 131, 200, 310, 485, 757, 1174, 1815, 2810, 4362, 6778, 10524, 16323, 25310, 39260, 60924, 94549, 146706, 227599, 353093, 547826, 850005, 1318859, 2046257, 3174775, 4925699, 7642389, 11857510

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {1,4,5,6}.

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 (1,0,0,1,1,1).

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

a(n) = a(n-1)+a(n-4)+a(n-5)+a(n-6).

G.f.: -1/(x^6+x^5+x^4+x-1).

A079964 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={0,4}.

Original entry on oeis.org

1, 0, 1, 1, 2, 2, 5, 5, 10, 13, 22, 30, 50, 70, 112, 163, 254, 375, 579, 862, 1320, 1979, 3015, 4536, 6893, 10392, 15764, 23800, 36064, 54492, 82521, 124748, 188841, 285561, 432174, 653642, 989097, 1496125, 2263754, 3424425, 5181150, 7837946

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {2,3,4,6}.

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 (0,1,1,1,0,1).

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

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

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

A079965 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={0,3}.

Original entry on oeis.org

1, 0, 1, 1, 1, 3, 3, 5, 8, 10, 17, 24, 35, 54, 77, 116, 172, 252, 377, 555, 822, 1220, 1801, 2671, 3953, 5849, 8666, 12823, 18987, 28113, 41612, 61615, 91214, 135037, 199929, 295976, 438193, 648734, 960420, 1421893, 2105059, 3116482, 4613879, 6830695

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {2,3,5,6}.

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 (0,1,1,0,1,1).

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

LinearRecurrence[{0,1,1,0,1,1},{1,0,1,1,1,3},50] (* Harvey P. Dale, Jul 10 2017 *)

a(n) = a(n-2)+a(n-3)+a(n-5)+a(n-6).

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

A079966 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={0,2}.

Original entry on oeis.org

1, 0, 1, 0, 2, 1, 4, 2, 7, 5, 14, 12, 27, 26, 53, 57, 106, 122, 212, 258, 428, 543, 868, 1135, 1766, 2364, 3605, 4910, 7374, 10175, 15109, 21054, 30998, 43513, 63656, 89851, 130817, 185416, 268984, 382436, 553308, 788520, 1138525, 1625356, 2343253

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {2,4,5,6}.

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 (0,1,0,1,1,1).

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

a(n) = a(n-2)+a(n-4)+a(n-5)+a(n-6).

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

A079967 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={4}.

Original entry on oeis.org

1, 1, 2, 4, 8, 15, 30, 58, 113, 220, 429, 835, 1627, 3169, 6173, 12024, 23422, 45623, 88869, 173107, 337194, 656817, 1279409, 2492150, 4854439, 9455922, 18419114, 35878442, 69887326, 136132954, 265172275, 516526919, 1006138588, 1959849178

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {1,2,3,4,6}.

Note that the number of compositions of n with parts in N which avoid the pattern 221 (see Heubach/Mansour) is not this sequence but A134044.

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.
S. Heubach and T. Mansour, Enumeration of 3-letter patterns in combinations, arXiv:math/0603285 [math.CO], 2006.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,0,1).

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

a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-6).

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

A079969 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={2}.

Original entry on oeis.org

1, 1, 2, 3, 6, 11, 21, 38, 70, 128, 236, 434, 799, 1469, 2702, 4969, 9140, 16811, 30921, 56872, 104604, 192396, 353872, 650872, 1197141, 2201885, 4049898, 7448923, 13700706, 25199527, 46349157, 85249390, 156798074, 288396620, 530444084

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {1,2,4,5,6}.

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 (1,1,0,1,1,1).

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

LinearRecurrence[{1,1,0,1,1,1},{1,1,2,3,6,11},40] (* Harvey P. Dale, Aug 03 2014 *)

a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5)+a(n-6).

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

A079995 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}.

Original entry on oeis.org

1, 1, 2, 4, 14, 39, 103, 255, 665, 1741, 4605, 12046, 31474, 82206, 215157, 563083, 1473635, 3855111, 10085589, 26386595, 69038554, 180630858, 472594580, 1236463719, 3235013481, 8463923170, 22144596592, 57937977232, 151585883920

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}.

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, 2, 3, 4, 6, 13, -9, -11, -7, 5, -1, -11, 3, 9, 4, -4, -1, 2, -1, -1).

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

CoefficientList[Series[-(x^14-x^12+x^11-x^10-x^9-x^8+3x^6-x^5+ x^4+ 3x^3+ x^2-1)/ (x^20+ x^19-2x^18+ x^17+4x^16-4x^15-9x^14- 3x^13+ 11x^12+ x^11- 5x^10+ 7x^9+11x^8+9x^7-13x^6-6x^5-4x^4-3x^3-2x^2-x+1),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,3,4,6,13,-9,-11,-7,5,-1,-11,3,9,4,-4,-1,2,-1,-1},{1,1,2,4,14,39,103,255,665,1741,4605,12046, 31474,82206,215157, 563083, 1473635,3855111,10085589,26386595},40] (* Harvey P. Dale, Oct 29 2017 *)

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

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

cp's OEIS Frontend

A079963 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={1,2}.

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A079964 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={0,4}.

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A079965 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={0,3}.

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A079966 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={0,2}.

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A079967 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={4}.

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A079969 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={2}.

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A079995 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}.

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