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.

Showing 1-3 of 3 results.

A361271 Number of 1342-avoiding odd Grassmannian permutations of size n.

Original entry on oeis.org

0, 0, 1, 2, 6, 9, 19, 25, 44, 54, 85, 100, 146, 167, 231, 259, 344, 380, 489, 534, 670, 725, 891, 957, 1156, 1234, 1469, 1560, 1834, 1939, 2255, 2375, 2736, 2872, 3281, 3434, 3894, 4065, 4579, 4769, 5340, 5550, 6181, 6412, 7106, 7359, 8119, 8395, 9224, 9524, 10425
Offset: 0

Views

Author

Juan B. Gil, Mar 07 2023

Keywords

Comments

A permutation is said to be Grassmannian if it has at most one descent. A permutation is odd if it has an odd number of inversions.
a(n) is also the number of 3124-avoiding odd Grassmannian permutations of size n.

Examples

			For n=4 the a(4)=6 permutations are 1243, 1324, 2134, 2341, 2413, 4123.

Links

Crossrefs

Cf. A356185, A361270, A361274.

Programs

  • PARI
    seq(n) = Vec(x^2*(x^4+x^2+x+1)/((1+x)^3*(1-x)^4) + O(x*x^n), -n-1) \\ Andrew Howroyd, Mar 07 2023

Formula

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

A361275 Number of 1423-avoiding even Grassmannian permutations of size n.

Original entry on oeis.org

1, 1, 1, 3, 5, 11, 17, 29, 41, 61, 81, 111, 141, 183, 225, 281, 337, 409, 481, 571, 661, 771, 881, 1013, 1145, 1301, 1457, 1639, 1821, 2031, 2241, 2481, 2721, 2993, 3265, 3571, 3877, 4219, 4561, 4941, 5321, 5741, 6161, 6623, 7085, 7591, 8097, 8649, 9201, 9801, 10401
Offset: 0

Views

Author

Juan B. Gil, Mar 10 2023

Keywords

Comments

A permutation is said to be Grassmannian if it has at most one descent. A permutation is even if it has an even number of inversions.
Avoiding any of the patterns 2314 or 3412 gives the same sequence.

Examples

			For n=4 the a(4) = 5 permutations are 1234, 1342, 2314, 3124, 3412.

Links

Crossrefs

Cf. A356185, A361272, A361273, A361274.
For the corresponding odd permutations, cf. A005993.

Programs

  • Maple
    seq(1 - 5*n/24 + n^3/12 - (-1)^n * n/8, n = 0 .. 100); # Robert Israel, Mar 10 2023

Formula

G.f.: -(x^5-x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
a(n) = 1 - 5*n/24 + n^3/12 - (-1)^n * n/8. - Robert Israel, Mar 10 2023

A361276 Number of 2413-avoiding even Grassmannian permutations of size n.

Original entry on oeis.org

1, 1, 1, 3, 6, 13, 22, 37, 55, 81, 111, 151, 196, 253, 316, 393, 477, 577, 685, 811, 946, 1101, 1266, 1453, 1651, 1873, 2107, 2367, 2640, 2941, 3256, 3601, 3961, 4353, 4761, 5203, 5662, 6157, 6670, 7221, 7791, 8401, 9031, 9703, 10396, 11133, 11892, 12697, 13525, 14401
Offset: 0

Views

Author

Juan B. Gil, Mar 10 2023

Keywords

Comments

A permutation is said to be Grassmannian if it has at most one descent. A permutation is even if it has an even number of inversions.

Examples

			For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.

Links

Crossrefs

Cf. A356185, A361272, A361273, A361274, A361275.
For the corresponding odd permutations, cf. A006918.

Programs

  • Mathematica
    LinearRecurrence[{2,1,-4,1,2,-1},{1,1,1,3,6,13},50] (* Harvey P. Dale, Aug 14 2023 *)

Formula

G.f.: -(x^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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