A001883 -id:A001883 - cp's OEIS frontend

A001889 Hit polynomials.

1, 4, 8, 38, 209, 1400, 10849, 95516, 938441, 10179149, 120748974, 1554688240, 21588485677, 321561688748, 5113709884902, 86469576394028, 1549114961438599, 29309613834899864, 583986501706555597, 12222118836543561940, 268060239251978779839, 6148136982942476816891

Offset: 2

N. J. A. Sloane

nonn

J. Riordan, The enumeration of permutations with three-ply staircase restrictions, unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963. (See A001883)
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, Annotated copy of Riordan's Three-Ply Staircase paper (unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963)

Third column of A080061.

Cf. A001883-A001891.

More terms from Vladeta Jovovic, Vladimir Baltic, Jan 23 2003

a(21)-a(23) from Vaclav Kotesovec, Oct 10 2017

A293044 Number of even permutations s of {1,2,...,n} such that |s(i)-i| > 1 for each i=1,2,...,n.

Original entry on oeis.org

1, 0, 0, 0, 1, 2, 14, 104, 854, 7850, 79870, 890348, 10799871, 141647372, 1997815108, 30156348224, 485117044079, 8285798537070, 149759338727580, 2855791585334780, 57300933786123530, 1206811729692494146, 26619251746350630604, 613691499376088985144

Offset: 0

Eric M. Schmidt, Oct 09 2017

nonn

Dmitry Efimov, Determinants of generalized binary band matrices, arXiv:1702.05655 [math.RA], 2017.

Cf. A001883, A293045.

a(n) = (A001883(n) + d(n))/2, where d(n) = (3-n)/3 if n = 0 mod 3, d(n) = (n-1)/3 if n = 1 mod 3, d(n) = 0 if n = 2 mod 3.

A293045 Number of odd permutations s of {1,2,...,n} such that |s(i)-i| > 1 for each i=1,2,...,n.

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 15, 102, 854, 7852, 79867, 890348, 10799874, 141647368, 1997815108, 30156348228, 485117044074, 8285798537070, 149759338727585, 2855791585334774, 57300933786123530, 1206811729692494152, 26619251746350630597, 613691499376088985144

Offset: 0

Eric M. Schmidt, Oct 09 2017

nonn

Dmitry Efimov, Determinants of generalized binary band matrices, arXiv:1702.05655 [math.RA], 2017.

Cf. A001883, A293044.

a(n) = (A001883(n) - d(n))/2, where d(n) = (3-n)/3 if n = 0 mod 3, d(n) = (n-1)/3 if n = 1 mod 3, d(n) = 0 if n = 2 mod 3.

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A001889 Hit polynomials.

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A293044 Number of even permutations s of {1,2,...,n} such that |s(i)-i| > 1 for each i=1,2,...,n.

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A293045 Number of odd permutations s of {1,2,...,n} such that |s(i)-i| > 1 for each i=1,2,...,n.

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Author

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Links

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Formula