A002529 -id:A002529 - cp's OEIS frontend

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}.

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).

A224814 Number of subsets of {1,2,...,n-9} without differences equal to 3, 6 or 9.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 12, 18, 27, 36, 48, 64, 80, 100, 125, 175, 245, 343, 490, 700, 1000, 1400, 1960, 2744, 3724, 5054, 6859, 9386, 12844, 17576, 24336, 33696, 46656, 64800, 90000, 125000, 172500, 238050, 328509, 452295, 622725, 857375, 1182275, 1630295, 2248091, 3106141, 4291691, 5929741, 8190250, 11312500, 15625000, 21562500

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=3, r=9, I={-3,0,9}.

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, 0, 1, 0, -1, 1, 0, -3, 4, 0, 5, -2, 0, 3, -8, 0, 1, -4, 0, 3, -4, 0, -3, 0, 0, -5, 8, 0, 7, -2, 0, -9, 2, 0, 5, 4, 0, 1, -6, 0, -3, 2, 0, 2, 1, 0, -1, -1, 0, 0, 1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808-A224815.

CoefficientList[Series[(1 - x^4 - x^5 - x^7 - x^8 + 2*x^9 - x^10 - 3*x^12 - x^13 - 2*x^15 + 3*x^16 + 3*x^17 + 2*x^18 - x^20 - 4*x^21 + x^23 + 3*x^24 + 3*x^25 + x^27 - 4*x^28 - x^29 - 2*x^30 + x^31 + 2*x^33 +x^34 - x^36 - x^37 + x^40)/((1 - x - x^4)*(1 - x^9 - x^12)*(1 + x^6 + 4*x^9 - 4*x^12 - 2*x^15 + 4*x^18 - 3*x^21 - 3*x^24 + 7*x^27 - 6*x^30 + 3*x^33 - x^36)), {x, 0, 50}], x] (* G. C. Greubel, Oct 28 2017 *)

x='x+O('x^50); Vec((1 -x^4 -x^5 -x^7 -x^8 +2*x^9 -x^10 -3*x^12 -x^13 -2*x^15 +3*x^16 +3*x^17 +2*x^18 -x^20 -4*x^21 +x^23 +3*x^24 +3*x^25 +x^27 -4*x^28 -x^29 -2*x^30 +x^31 +2*x^33 +x^34 -x^36 -x^37 +x^40 )/((1-x-x^4)*(1-x^9-x^12)*(1 +x^6 +4*x^9 -4*x^12 -2*x^15 +4*x^18 -3*x^21 -3*x^24 +7*x^27 -6*x^30 +3*x^33 -x^36))) \\ G. C. Greubel, Oct 28 2017

a(n) = a(n-1) +a(n-4) -a(n-6) +a(n-7) -3*a(n-9) +4*a(n-10) +5*a(n-12) -2*a(n-13) +3*a(n-15) -8*a(n-16) +a(n-18) -4*a(n-19) +3*a(n-21) -4*a(n-22) -3*a(n-24) -5*a(n-27) +8*a(n-28) +7*a(n-30) -2*a(n-31) -9*a(n-33) +2*a(n-34) +5*a(n-36) +4*a(n-37) +a(n-39) -6*a(n-40) -3*a(n-42) +2*a(n-43) +2*a(n-45) +a(n-46) -a(n-48) -a(n-49) +a(n-52).
G.f.: (1 -x^4 -x^5 -x^7 -x^8 +2*x^9 -x^10 -3*x^12 -x^13 -2*x^15 +3*x^16 +3*x^17 +2*x^18 -x^20 -4*x^21 +x^23 +3*x^24 +3*x^25 +x^27 -4*x^28 -x^29 -2*x^30 +x^31 +2*x^33 +x^34 -x^36 -x^37 +x^40 )/((1-x-x^4)*(1-x^9-x^12)*(1 +x^6 +4*x^9 -4*x^12 -2*x^15 +4*x^18 -3*x^21 -3*x^24 +7*x^27 -6*x^30 +3*x^33 -x^36)).
a(3*k) = (A003269(k))^3,
a(3*k+1) = (A003269(k))^2 * A003269(k+1),
a(3*k+2) = A003269(k) * (A003269(k+1))^2.

A079816 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}.

Original entry on oeis.org

1, 1, 1, 2, 4, 7, 12, 20, 34, 59, 102, 175, 300, 515, 885, 1521, 2613, 4488, 7709, 13243, 22750, 39081, 67134, 115324, 198107, 340315, 584604, 1004250, 1725130, 2963480, 5090756, 8745055, 15022519, 25806135, 44330556, 76152366, 130816831

Offset: 0

Vladimir Baltic, Feb 19 2003

nonn

Number of compositions (ordered partitions) of n into elements of the set {1,3,4,5,6}.

a(n+1) is the number of multus bitstrings of length n with no runs of 6 ones. - Steven Finch, Mar 25 2020

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.

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 (2010), 119-135
Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1,1,1).

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

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^3-x^4-x^5-x^6) )); // G. C. Greubel, Dec 12 2023

LinearRecurrence[{1,0,1,1,1,1}, {1,1,1,2,4,7}, 51] (* G. C. Greubel, Dec 12 2023 *)

def A079816_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x-x^3-x^4-x^5-x^6) ).list()
A079816_list(50) # G. C. Greubel, Dec 12 2023

Recurrence: a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6).

G.f.: 1/(1-x-x^3-x^4-x^5-x^6).

A079956 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={0,1,4}.

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 2, 2, 1, 3, 5, 3, 6, 10, 9, 12, 21, 22, 27, 43, 52, 61, 91, 117, 140, 195, 260, 318, 426, 572, 718, 939, 1258, 1608, 2083, 2769, 3584, 4630, 6110, 7961, 10297, 13509, 17655, 22888, 29916, 39125, 50840, 66313, 86696, 112853, 147069, 192134

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {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 (0,0,1,1,0,1).

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

LinearRecurrence[{0,0,1,1,0,1},{1,0,0,1,1,0},60] (* Harvey P. Dale, Oct 05 2016 *)

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

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

A079976 Expansion of g.f. 1/(1-x-x^2-x^4-x^5).

Original entry on oeis.org

1, 1, 2, 3, 6, 11, 20, 36, 65, 118, 214, 388, 703, 1274, 2309, 4185, 7585, 13747, 24915, 45156, 81841, 148329, 268832, 487232, 883061, 1600463, 2900685, 5257212, 9528190, 17268926, 31298264, 56725087, 102808753, 186330956, 337706899

Offset: 0

Vladimir Baltic, Feb 17 2003

nonn

Number of compositions of n into elements of the set {1,2,4,5}.

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

Kassie Archer and Aaron Geary, Powers of permutations that avoid chains of patterns, arXiv:2312.14351 [math.CO], 2023. See p. 15.
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135
Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,1)

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

CoefficientList[Series[1/(1-x-x^2-x^4-x^5),{x,0,40}],x] (* or *) LinearRecurrence[ {1,1,0,1,1},{1,1,2,3,6},40] (* Harvey P. Dale, Mar 16 2023 *)

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

Since this sequence arises in several different contexts, I made the definition as simple as possible. - N. J. A. Sloane, Apr 17 2011

A079981 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={-2,0,1,2}.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 2, 0, 3, 0, 8, 0, 12, 0, 27, 0, 52, 0, 95, 0, 196, 0, 369, 0, 720, 0, 1408, 0, 2709, 0, 5292, 0, 10249, 0, 19894, 0, 38675, 0, 74992, 0, 145692, 0, 282823, 0, 549000, 0, 1066095, 0, 2069496, 0, 4018065, 0, 7801024, 0, 15144960, 0, 29404281, 0

Offset: 0

Vladimir Baltic, Feb 17 2003

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,-1,0,2}. a(n)=A079980(k) if n=2k, a(n)=0 otherwise.

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 (0,0,0,1,0,4,0,2,0,2,0,-2,0,1,0,0,0,1).

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

Bisection gives A079980 (even part).

LinearRecurrence[{0,0,0,1,0,4,0,2,0,2,0,-2,0,1,0,0,0,1},{1,0,0,0,1,0,2,0,3,0,8,0,12,0,27,0,52,0},80] (* Harvey P. Dale, Aug 18 2012 *)

Recurrence: a(n) = a(n-4)+4*a(n-6)+2*a(n-8)+2*a(n-10)-2*a(n-12)+a(n-14)+a(n-18).

G.f.: -(x^12-2*x^6+1)/(x^18+x^14-2*x^12+2*x^10+2*x^8+4*x^6+x^4-1).

A079989 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={1,2}.

Original entry on oeis.org

1, 1, 1, 1, 5, 13, 27, 51, 103, 221, 498, 1064, 2240, 4728, 10076, 21559, 46075, 98085, 208759, 444727, 948151, 2021335, 4307861, 9179111, 19560273, 41686260, 88842852, 189337896, 403497908, 859893060, 1832537757, 3905386173, 8322891733, 17737112293, 37799944529

Offset: 0

Vladimir Baltic, Feb 17 2003

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,-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.

Stefano Spezia, Table of n, a(n) for n = 0..3000
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 (1,1,2,1,3,4,-7,-7,-6,6,-2,-1,1,4,1,-3,0,1,-1,-1).

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

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

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

A224812 Number of subsets of {1,2,...,n-10} without differences equal to 2, 4, 6, 8 or 10.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 63, 81, 108, 144, 192, 256, 336, 441, 567, 729, 918, 1156, 1462, 1849, 2365, 3025, 3905, 5041, 6532, 8464, 10948, 14161, 18207, 23409, 29988, 38416, 49196, 63001, 80822, 103684, 133308, 171396, 220662, 284089, 365638, 470596, 605052, 777924, 999306, 1283689, 1648515

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=2, r=10, I={-2,0,10}.

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, 0, 0, 0, 0, 1, -1, 1, -1, 1, 3, -2, 2, -1, 1, 0, 0, -2, 1, -2, 0, 0, -3, 1, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808-A224815.

CoefficientList[Series[-(x + 1)*(x^23 - x^22 + x^21 - x^20 + x^19 - x^13 + x^12 - 3*x^11 + 3*x^10 - 3*x^9 + 2*x^8 - 2*x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)/((x^6 + x - 1)*(x^30 + x^24 - 2*x^20 - 2*x^18 - x^14 - 2*x^12 + x^10 + x^8 + x^6 + 1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 28 2017 *)

x='x+O('x^50); Vec(-(x + 1)*(x^23 - x^22 + x^21 - x^20 + x^19 - x^13 + x^12 - 3*x^11 + 3*x^10 - 3*x^9 + 2*x^8 - 2*x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)/((x^6 + x - 1)*(x^30 + x^24 - 2*x^20 - 2*x^18 - x^14 - 2*x^12 + x^10 + x^8 + x^6 + 1))) \\ G. C. Greubel, Oct 28 2017

a(n) = a(n-1) +a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11) +3*a(n-12) -2*a(n-13) +2*a(n-14) -a(n-15) +a(n-16) -2*a(n-19) +a(n-20) -2*a(n-21) -3*a(n-24) +a(n-25) -2*a(n-26) +a(n-31) +a(n-36).
G.f.: -(x+1) *(x^23 -x^22 +x^21 -x^20 +x^19 -x^13 +x^12 -3*x^11 +3*x^10 -3*x^9 +2*x^8 -2*x^7 +x^6 -x^5 +x^4 -x^3 +x^2 -x +1)/ ((x^6 +x -1) *(x^30 +x^24 -2*x^20 -2*x^18 -x^14 -2*x^12 +x^10 +x^8 +x^6+1) ).
a(2*k) = (A005708(k))^2, a(2*k+1) = A005708(k) * A005708(k+1).

A224813 Number of subsets of {1,2,...,n-12} without differences equal to 2, 4, 6, 8, 10 or 12.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 80, 100, 130, 169, 221, 289, 374, 484, 616, 784, 980, 1225, 1505, 1849, 2279, 2809, 3498, 4356, 5478, 6889, 8715, 11025, 13965, 17689, 22344, 28224, 35448, 44521, 55704, 69696, 87120, 108900, 136290, 170569, 213934, 268324, 337218, 423801, 533169, 670761, 843570

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=2, r=12, I={-2,0,12}.

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, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, 3, -2, 2, -1, 1, 0, 0, -3, 2, -4, 2, -3, 0, 0, -3, 1, -2, 0, 0, 0, 0, 3, -1, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1).

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808-A224815.

CoefficientList[Series[-(-1 + x^7 + x^9 + x^11 + 2*x^14 + x^16 - 2*x^21 - 2*x^23 - x^28 + x^35)/((x^7 + x - 1)*(x^42 - x^36 - 2*x^30 - 3*x^28 + 2*x^24 + 2*x^22 + x^18 + 2*x^16 + 3*x^14 - x^12 - x^10 - x^8 - 1)), {x, 0, 1000}], x] (* G. C. Greubel, Oct 28 2017 *)

x='x+O('x^50); Vec(-(-1 + x^7 + x^9 + x^11 + 2*x^14 + x^16 - 2*x^21 - 2*x^23 - x^28 + x^35)/((x^7 + x - 1)*(x^42 - x^36 - 2*x^30 - 3*x^28 + 2*x^24 + 2*x^22 + x^18 + 2*x^16 + 3*x^14 - x^12 - x^10 - x^8 - 1))) \\ G. C. Greubel, Oct 28 2017

a(n) = a(n-1) +a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11) -a(n-12) +a(n-13) +3*a(n-14) -2*a(n-15) +2*a(n-16) -a(n-17) +a(n-18) -3*a(n-21) +2*a(n-22) -4*a(n-23) +2*a(n-24) -3*a(n-25) -3*a(n-28) +a(n-29) -2*a(n-30) +3*a(n-35) -a(n-36) +3*a(n-37) +a(n-42) -a(n-49).
G.f.: -(-1 +x^7 +x^9 +x^11 +2*x^14 +x^16 -2*x^21 -2*x^23 -x^28 +x^35)/( (x^7+x-1) *(x^42 -x^36 -2*x^30 -3*x^28 +2*x^24 +2*x^22 +x^18 +2*x^16 +3*x^14 -x^12 -x^10 -x^8 -1) ).
a(2*k) = (A005709(k))^2, a(2*k+1) = A005709(k) * A005709(k+1).

A079968 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}.

Original entry on oeis.org

1, 1, 2, 4, 7, 14, 27, 51, 98, 187, 357, 683, 1305, 2494, 4767, 9110, 17411, 33276, 63596, 121544, 232293, 443954, 848478, 1621597, 3099169, 5923081, 11320094, 21634776, 41348026, 79023662, 151028714, 288643577, 551650823, 1054305916

Offset: 0

Vladimir Baltic, Feb 19 2003

Number of compositions (ordered partitions) of n into elements of the set {1,2,3,5,6}.

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.

D. Applegate, M. LeBrun, N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
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 (1,1,1,0,1,1).

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

LinearRecurrence[{1,1,1,0,1,1},{1,1,2,4,7,14},40] (* Harvey P. Dale, Jun 05 2013 *)

a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-5)+a(n-6).

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

cp's OEIS Frontend

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}.

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A224814 Number of subsets of {1,2,...,n-9} without differences equal to 3, 6 or 9.

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A079816 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}.

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A079956 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={0,1,4}.

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A079976 Expansion of g.f. 1/(1-x-x^2-x^4-x^5).

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A079981 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={-2,0,1,2}.

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A079989 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={1,2}.

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A224812 Number of subsets of {1,2,...,n-10} without differences equal to 2, 4, 6, 8 or 10.

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