A369906 Sum of the permanents of all 2 X 2 submatrices in the n X n Pascal matrix.
0, 0, 1, 9, 50, 234, 1016, 4256, 17509, 71349, 289223, 1168815, 4714425, 18991401, 76434373, 307411285, 1235697666, 4964876706, 19940653388, 80062371380, 321361753426, 1289589924226, 5173842730758, 20753408180790, 83231772855896, 333749033253560
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1661
- Wikipedia, Permanent (mathematics)
Programs
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Maple
a:= proc(n) option remember; `if`(n<5, [0, 0, 1, 9, 50][n+1], ((13*n-12)*a(n-1)-8*(8*n-15)*a(n-2)+4*(37*n-105)* a(n-3)-40*(4*n-15)*a(n-4)+32*(2*n-9)*a(n-5))/n) end: seq(a(n), n=0..32);
Formula
a(n) ~ 4^n/3 * (1 - 1/sqrt(Pi*n)). - Vaclav Kotesovec, Feb 19 2024