cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A080006 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={0,2}.

Original entry on oeis.org

1, 0, 1, 1, 3, 5, 8, 16, 27, 51, 91, 164, 298, 536, 972, 1755, 3172, 5735, 10363, 18735, 33861, 61204, 110628, 199957, 361427, 653277, 1180800, 2134300, 3857748, 6972892, 12603513, 22780876, 41176481, 74426569, 134526179, 243156337
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Formula

a(n) = a(n-2)+2*a(n-3)+2*a(n-4)+3*a(n-5)+a(n-6)-a(n-8)-a(n-9)-a(n-10).
G.f.: -(x^5+x^3-1)/(x^10+x^9+x^8-x^6-3*x^5-2*x^4-2*x^3-x^2+1)

A080007 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={0,1}.

Original entry on oeis.org

1, 0, 0, 1, 2, 4, 4, 8, 19, 32, 56, 97, 180, 336, 592, 1064, 1925, 3488, 6312, 11345, 20486, 37028, 66852, 120688, 217767, 393216, 710032, 1281729, 2313896, 4177216, 7541568, 13615344, 24579657, 44374528, 80111088, 144628065, 261102474
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Formula

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

A080008 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}.

Original entry on oeis.org

1, 0, 0, 1, 2, 2, 3, 5, 11, 15, 24, 40, 68, 110, 177, 290, 480, 783, 1278, 2090, 3427, 5609, 9171, 15005, 24564, 40200, 65776, 107628, 176137, 288244, 471676, 771845, 1263074, 2066938, 3382367, 5534941, 9057495, 14821891, 24254820, 39691008
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Formula

Recurrence: a(n) = a(n-2)+a(n-3)+2*a(n-4)+2*a(n-5)-a(n-7)-a(n-9)-a(n-10).
G.f.: -(x^5+x^2-1)/((x^9+x^6-x^5-x^4-x^3-x+1)*(x+1))

A080009 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={2}.

Original entry on oeis.org

1, 1, 2, 4, 11, 26, 56, 127, 288, 660, 1500, 3401, 7729, 17565, 39930, 90735, 206176, 468536, 1064750, 2419661, 5498621, 12495505, 28395889, 64529315, 146642077, 333242093, 757288191, 1720927502, 3910785158, 8887207808, 20196062308
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Programs

  • Mathematica
    LinearRecurrence[{1,1,2,3,5,0,1,-1,-1,-1},{1,1,2,4,11,26,56,127,288,660},40] (* Harvey P. Dale, Nov 20 2021 *)

Formula

a(n) = a(n-1)+a(n-2)+2*a(n-3)+3*a(n-4)+5*a(n-5)+a(n-7)-a(n-8)-a(n-9)-a(n-10).
G.f.: -(x^5+x^3-1)/(x^10+x^9+x^8-x^7-5*x^5-3*x^4-2*x^3-x^2-x+1)

A080010 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}.

Original entry on oeis.org

1, 1, 1, 3, 9, 19, 38, 84, 193, 430, 940, 2074, 4609, 10223, 22611, 50022, 110780, 245348, 543189, 1202511, 2662417, 5894961, 13051820, 28897016, 63979205, 141653762, 313629217, 694390210, 1537413824, 3403913006, 7536438344
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Formula

Recurrence: a(n) = a(n-1)+a(n-2)+2*a(n-3)+3*a(n-4)+3*a(n-5)-2*a(n-6)-a(n-7)-a(n-10).
G.f.: -(x^5+x^3+x^2-1)/(x^10+x^7+2*x^6-3*x^5-3*x^4-2*x^3-x^2-x+1).

A080011 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}.

Original entry on oeis.org

1, 1, 1, 3, 7, 15, 29, 59, 126, 262, 542, 1121, 2328, 4839, 10039, 20827, 43220, 89704, 186172, 386345, 801768, 1663916, 3453137, 7166272, 14872078, 30863935, 64051787, 132926308, 275861116, 572492846, 1188091024, 2465638247
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Programs

  • Mathematica
    LinearRecurrence[{1,1,1,2,3,-1,0,1,-1,-1},{1,1,1,3,7,15,29,59,126,262},40] (* Harvey P. Dale, Nov 03 2022 *)

Formula

a(n) = a(n-1)+a(n-2)+a(n-3)+2*a(n-4)+3*a(n-5)-a(n-6)+a(n-8)-a(n-9)-a(n-10).
G.f.: -(x^5+x^2-1)/(x^10+x^9-x^8+x^6-3*x^5-2*x^4-x^3-x^2-x+1)

A080012 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={0}.

Original entry on oeis.org

1, 0, 1, 2, 6, 11, 23, 51, 113, 244, 526, 1142, 2483, 5389, 11687, 25358, 55034, 119430, 259151, 562340, 1220276, 2647993, 5746085, 12468857, 27057165, 58713537, 127407187, 276470942, 599936262, 1301849496, 2824986880, 6130163753
Offset: 0

Views

Author

Vladimir Baltic, Feb 10 2003

Keywords

References

  • 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.

Links

Crossrefs

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

Formula

a(n) = 2a(n-2)+3a(n-3)+4a(n-4)+5a(n-5)+a(n-6)-2a(n-7)-a(n-8)-a(n-9)-a(n-10).
G.f.: -(x^5+x^3+x^2-1)/(x^10+x^9+x^8+2*x^7-x^6-5*x^5-4*x^4-3*x^3-2*x^2+1)

A079959 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={2,4}.

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 19, 33, 60, 106, 191, 340, 610, 1089, 1950, 3485, 6236, 11150, 19946, 35670, 63802, 114107, 204091, 365018, 652857, 1167652, 2088402, 3735179, 6680529, 11948378, 21370166, 38221375, 68360472, 122265404, 218676571
Offset: 0

Views

Author

Vladimir Baltic, Feb 19 2003

Keywords

Comments

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

References

  • 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.

Links

Crossrefs

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

Formula

a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-6).
G.f.: -1/(x^6+x^4+x^2+x-1).

A079960 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={2,3}.

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 16, 28, 49, 85, 148, 258, 450, 785, 1369, 2387, 4162, 7257, 12654, 22065, 38475, 67089, 116983, 203983, 355685, 620208, 1081457, 1885737, 3288160, 5733565, 9997618, 17432848, 30397660, 53004405, 92423790, 161159378
Offset: 0

Views

Author

Vladimir Baltic, Feb 19 2003

Keywords

Comments

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

References

  • 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.

Links

Crossrefs

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

Programs

  • Maple
    g:=1/(1-z-z^2-z^5-z^6): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=0..35); # Zerinvary Lajos, Apr 17 2009

Formula

a(n) = a(n-1) + a(n-2) + a(n-5) + a(n-6).
G.f.: -1/(x^6 + x^5 + x^2 + x - 1).

A079961 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={1,4}.

Original entry on oeis.org

1, 1, 1, 2, 4, 6, 10, 17, 28, 46, 77, 128, 212, 352, 585, 971, 1612, 2677, 4445, 7380, 12254, 20347, 33784, 56095, 93141, 154652, 256785, 426368, 707945, 1175477, 1951771, 3240736, 5380943, 8934559, 14835011, 24632167, 40899440, 67909746
Offset: 0

Views

Author

Vladimir Baltic, Feb 19 2003

Keywords

Comments

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

References

  • 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.

Links

Crossrefs

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

Programs

  • Maple
    g:=1/(1-z-z^3-z^4-z^6): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=0..37); # Zerinvary Lajos, Apr 17 2009

Formula

a(n) = a(n-1)+a(n-3)+a(n-4)+a(n-6).
G.f.: -1/(x^6+x^4+x^3+x-1).
Previous Showing 61-70 of 77 results. Next

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