A218268
Number of standard Young tableaux of n cells and height >= 8.
Original entry on oeis.org
1, 9, 81, 561, 3817, 23881, 147862, 886028, 5288933, 31178901, 183908244, 1081452450, 6381113064, 37719710024, 224141652938, 1337958249446, 8038507929319, 48593807722975, 295913856459150, 1814986751559300, 11220842616565050, 69921225307663290
Offset: 8
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b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
((4*n^3+78*n^2+424*n+495)*g(n-1) +(n-1)*(34*n^2+280*n
+305)*g(n-2) -2*(n-1)*(n-2)*(38*n+145)*g(n-3) -105*(n-1)
*(n-2)*(n-3)*g(n-4)) / ((n+6)*(n+10)*(n+12)))
end:
a:= n-> b(n) -g(n):
seq(a(n), n=8..30);
A218269
Number of standard Young tableaux of n cells and height >= 9.
Original entry on oeis.org
1, 10, 100, 760, 5656, 38416, 257376, 1660416, 10640692, 67100072, 422374352, 2643349180, 16566306380, 103786892840, 652502735152, 4113403313016, 26057914447911, 165824119892086, 1061381766546172, 6832087071296824, 44260892997918920, 288574772339715376
Offset: 9
-
b:= proc(n) b(n):= `if`(n<2, 1, b(n-1) +(n-1)*b(n-2)) end:
g:= proc(n) option remember; `if`(n<4, [1, 1, 2, 4][n+1],
((40*n^3+1084*n^2+8684*n+18480)*g(n-1) +16*(n-1)
*(5*n^3+107*n^2+610*n+600)*g(n-2) -1024*(n-1)*(n-2)
*(n+6)*g(n-3) -1024*(n-1)*(n-2)*(n-3)*(n+4)*g(n-4))/
((n+7)*(n+12)*(n+15)*(n+16)))
end:
a:= n-> b(n) -g(n):
seq(a(n), n=9..30);
A229068
Number of standard Young tableaux of n cells and height <= 12.
Original entry on oeis.org
1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140152, 568503, 2390466, 10349340, 46204720, 211779200, 997134592, 4808141824, 23745792032, 119848119307, 618058083314, 3251373425356, 17442275104496, 95297400355320, 530067682582320, 2998503402985440
Offset: 0
Cf.
A182172,
A001405 (k=2),
A001006 (k=3),
A005817 (k=4),
A049401 (k=5),
A007579 (k=6),
A007578 (k=7),
A007580 (k=8),
A212915 (k=9),
A212916 (k=10),
A229053 (k=11).
-
RecurrenceTable[{-147456 (-5+n) (-4+n) (-3+n) (-2+n) (-1+n) (12+n) a[-6+n]-110592 (-4+n) (-3+n) (-2+n) (-1+n) (29+2 n) a[-5+n]+256 (-3+n) (-2+n) (-1+n) (121272+32786 n+2343 n^2+49 n^3) a[-4+n]+128 (-2+n) (-1+n) (438597+90321 n+5391 n^2+98 n^3) a[-3+n]-16 (-1+n) (8718630+5347213 n+804616 n^2+49754 n^3+1372 n^4+14 n^5) a[-2+n]-8 (27335490+10162354 n+1206473 n^2+63328 n^3+1533 n^4+14 n^5) a[-1+n]+(11+n) (20+n) (27+n) (32+n) (35+n) (36+n) a[n]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==10, a[5]==26, a[6]==76}, a, {n, 20}]
Comments