Jessica A. Tomasko - cp's OEIS frontend

A362197 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 10 with exactly one descent.

1, 1, 2, 5, 12, 27, 58, 121, 248, 503, 1013, 2025, 4005, 7801, 14899, 27809, 50627, 89829, 155364, 262125, 431890, 695839, 1097768, 1698137, 2579106, 3850731, 5658511, 8192497, 11698195, 16489517, 22964057, 31620993, 43081941, 58115113, 77663158, 102875093

Offset: 0

Jessica A. Tomasko, Apr 29 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 10 with exactly one descent. For example, sigma can be chosen to be 124789356(10), 247913568(10), 36(10)1245789, 57(10)1234689, etc.

J. B. Gil and J. Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A000325, A362196.

a(n) = 1 + Sum_{i=2..9} binomial(n,i).

G.f.: (1-9*x+37*x^2-90*x^3+142*x^4-150*x^5+106*x^6-48*x^7+13*x^8-x^9)/(1-x)^10.

A362196 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 9 with exactly one descent.

Original entry on oeis.org

1, 1, 2, 5, 12, 27, 58, 121, 248, 502, 1003, 1970, 3785, 7086, 12897, 22804, 39187, 65519, 106744, 169747, 263930, 401909, 600348, 880947, 1271602, 1807756, 2533961, 3505672, 4791295, 6474512, 8656907, 11460918, 15033141, 19548013, 25211902, 32267633, 40999480

Offset: 0

Jessica A. Tomasko, Apr 20 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 9 with exactly one descent. For example, sigma can be chosen to be 124793568, 248135679, 367912458, 591234678, etc.

Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A000325, A362195.

Table[1 + Sum[Binomial[n, i-1],{i,3,9}],{n,0,36}] (* Stefano Spezia, Apr 20 2023 *)

a(n) = 1 + Sum_{i=2..8} binomial(n,i).
G.f.: (1-8*x+29*x^2-61*x^3+81*x^4-69*x^5+37*x^6-11*x^7+2*x^8)/(1-x)^9.
a(n) = (n^8-20*n^7+210*n^6-1064*n^5+3969*n^4-4340*n^3+15980*n^2-14736*n+40320)/8!. - Alois P. Heinz, Apr 21 2023

A362195 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 8 with exactly one descent.

Original entry on oeis.org

1, 1, 2, 5, 12, 27, 58, 121, 247, 493, 958, 1805, 3290, 5799, 9894, 16369, 26317, 41209, 62986, 94165, 137960, 198419, 280578, 390633, 536131, 726181, 971686, 1285597, 1683190, 2182367, 2803982, 3572193, 4514841, 5663857, 7055698, 8731813, 10739140, 13130635

Offset: 0

Jessica A. Tomasko, Apr 20 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 8 with exactly one descent. For example, sigma can be chosen to be 12473568, 24781356, 36124578, 58123467, etc.

Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A000325, A362194.

Table[1 + Sum[Binomial[n, i-1],{i,3,8}],{n,0,37}] (* Stefano Spezia, Apr 20 2023 *)

a(n) = 1 + Sum_{i=3..8} binomial(n, i-1).

G.f.: (1-7*x+22*x^2-39*x^3+42*x^4-27*x^5+10*x^6-x^7)/(1-x)^8.

A362194 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 7 with exactly one descent.

Original entry on oeis.org

1, 1, 2, 5, 12, 27, 58, 120, 239, 457, 838, 1475, 2498, 4083, 6462, 9934, 14877, 21761, 31162, 43777, 60440, 82139, 110034, 145476, 190027, 245481, 313886, 397567, 499150, 621587, 768182, 942618, 1148985, 1391809, 1676082, 2007293, 2391460, 2835163, 3345578, 3930512

Offset: 0

Jessica A. Tomasko, Apr 20 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 7 with exactly one descent. For example, sigma can be chosen to be 1247356, 2413567, 3671245, 5712346, etc.

Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A000325, A008859, A362193.

a(n) = 1 + sum(i=2, 6, binomial(n,i)) \\ Andrew Howroyd, Apr 20 2023

a(n) = 1 + Sum_{i=2..6} binomial(n, i).
a(n) = A008859(n) - n.
G.f.: (1-6*x+16*x^2-23*x^3+19*x^4-8*x^5+2*x^6)/(1-x)^7.
E.g.f.: exp(x)*(720 + 360*x^2 + 120*x^3 + 30*x^4 + 6*x^5 + x^6)/720. - Stefano Spezia, Apr 20 2023

A362193 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 6 with exactly one descent.

Original entry on oeis.org

1, 1, 2, 5, 12, 27, 57, 113, 211, 373, 628, 1013, 1574, 2367, 3459, 4929, 6869, 9385, 12598, 16645, 21680, 27875, 35421, 44529, 55431, 68381, 83656, 101557, 122410, 146567, 174407, 206337, 242793, 284241, 331178, 384133, 443668, 510379, 584897

Offset: 0

Jessica A. Tomasko, Apr 10 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 6 with exactly one descent. For example, sigma can be chosen to be 124356, 241356, 361245, 512346, etc.

Juan B. Gil and Jessica A. Tomasko, Restricted Grassmannian permutations, Enum. Combin. Appl. 2 (2022), no. 4, Article #S4PP6.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A027660, A361270, A361271, A356185, A000325, A027927.

a:= n-> 1+(n-1)*n*(n+1)*(n*(n-5)+26)/120:
seq(a(n), n=0..38);  # Alois P. Heinz, Apr 12 2023

CoefficientList[Series[(1 - 5 x + 11 x^2 - 12 x^3 + 7 x^4 - x^5)/(1 - x)^6, {x, 0, 38}], x] (* Michael De Vlieger, Apr 12 2023 *)

a(n) = 1 + sum(i=3, 6, binomial(n, i-1)) \\ Andrew Howroyd, Apr 10 2023

a(n) = 1 + Sum_{i=2..5} binomial(n,i).
G.f.: (1-5*x+11*x^2-12*x^3+7*x^4-x^5)/(1-x)^6.
a(0) = 1; a(1) = 1; a(n) = 1 + A027660(n-2), n >= 2. - Omar E. Pol, Apr 12 2023

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User: Jessica A. Tomasko

A362197 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 10 with exactly one descent.

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A362196 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 9 with exactly one descent.

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A362195 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 8 with exactly one descent.

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A362194 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 7 with exactly one descent.

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A362193 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 6 with exactly one descent.

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