A177304
Number of permutations of 6 copies of 1..n with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 1, 924, 65226, 7426610, 640160976, 54331653686, 4339892975512, 336181036999948, 25328979140590460, 1869147741803280158, 135594223551932310368, 9700134237572864570026, 685890678156217774839644, 48025674779522388568648420, 3334799454210630503054336064
Offset: 0
A177307
Number of permutations of 7 copies of 1..n with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 1, 3432, 623576, 201922730, 48203722464, 11408205434138, 2535604038015218, 546641872918476120, 114573118435555703030, 23513682407867601161354, 4742254932865402388419776, 942857462878069039167940082, 185226548794692635344238756018, 36021105095432337381819132791160
Offset: 0
A177310
Number of permutations of 8 copies of 1..n with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 1, 12870, 6077196, 5650739930, 3772321496064, 2514046004253110, 1570273521448103668, 951645881858020642746, 560523113474283819256640, 323221203836407773725200718, 183122229346363470922528553652, 102256611847518844993947706000234
Offset: 0
A177313
Number of permutations of 9 copies of 1..n with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 1, 48620, 60110030, 161686253810, 304100156874800, 574996024253854586, 1016915629343040544250, 1745708356607370063330620, 2911820015993491302722966990, 4754502826758413615581742528138, 7626389809822483147908697112197520, 12055478550658617275428327115583119762
Offset: 0
A177318
Number of permutations of n copies of 1..6 with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 2, 86, 10010, 1543862, 276285002, 54331653686, 11408205434138, 2514046004253110, 574996024253854586, 135442141147145037086, 32677132473420748546466, 8041851882854648557516118, 2012484136612620102100796090, 510873291048466091968494930086
Offset: 0
A177319
Number of permutations of n copies of 1..7 with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 2, 148, 41618, 16699380, 8039989002, 4339892975512, 2535604038015218, 1570273521448103668, 1016915629343040544250, 682308706348352869913148, 471167961102713571612302730, 333217453890900855796193690520, 240438319207137787818120695999370
Offset: 0
A177320
Number of permutations of n copies of 1..8 with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 2, 250, 168284, 175280570, 226901044252, 336181036999948, 546641872918476120, 951645881858020642746, 1745708356607370063330620, 3337797628633312532069739500, 6600171805939224952685745226312, 13419910030462066174528563412581260, 27933944205209773363718168619462715544
Offset: 0
A177321
Number of permutations of n copies of 1..9 with all adjacent differences <= 1 in absolute value.
Original entry on oeis.org
1, 2, 416, 664958, 1792874048, 6232521421502, 25328979140590460, 114573118435555703030, 560523113474283819256640, 2911820015993491302722966990, 15861703283168731825003935183416, 89796737967084981726163781067177194, 524830705066715697873367329722967841532
Offset: 0
A331623
Number of sequences with n copies each of 1,2,...,n avoiding absolute differences between adjacent elements larger than one.
Original entry on oeis.org
1, 1, 6, 92, 11482, 8956752, 54331653686, 2535604038015218, 951645881858020642746, 2911820015993491302722966990, 73784388170659542104264761249115686, 15642058800086197220958447712819197014917632, 27980772370697320617389378491983217784996780441605354
Offset: 0
a(0) = 1: the empty sequence.
a(1) = 1: 1.
a(2) = 6: 1122, 1212, 1221, 2112, 2121, 2211.
a(3) = 92: 111222333, 111223233, 111223323, 111223332, ..., 333221112, 333221121, 333221211, 333222111.
-
b:= proc(l, q) option remember; (n-> `if`(n<2, 1, add(
`if`(l[j]=1, `if`(j in [1, n], b(subsop(j=[][], l),
`if`(j=1, 0, n)), 0), b(subsop(j=l[j]-1, l), j)), j=
`if`(q<0, 1..n, max(1, q-1)..min(n, q+1)))))(nops(l))
end:
a:= n-> b([n$n], -1):
seq(a(n), n=0..6);
-
b[l_, q_] := b[l, q] = With[{n = Length[l]}, If[n < 2, 1, Sum[
If[l[[j]] == 1, If[j == 1 || j == n, b[ReplacePart[l, j -> Nothing],
If[j == 1, 0, n]], 0], b[ReplacePart[l, j -> l[[j]] - 1], j]], {j,
If[q < 0, Range[n], Range[Max[1, q - 1], Min[n, q + 1]]]}]]];
a[n_] := b[Table[n, {n}], -1];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 8}] (* Jean-François Alcover, Jan 04 2021, after Alois P. Heinz *)
Comments