A263160
Number of lattice paths starting at {n}^n and ending when n or any component equals 0 and using steps that decrement one or more components by one.
Original entry on oeis.org
1, 1, 13, 5419, 328504401, 7622403922836151, 125076804896889941384267749, 2283244029676857615289372083169016508547, 66656513992169790340795231563272399566454175106315563265, 4218602489837041203989313097616905233039652652837921715487541815010092122991
Offset: 0
A263162
Number of lattice paths starting at {n}^4 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 15, 2101, 717795, 328504401, 172924236255, 98788351385893, 59547100211425779, 37279994808479614465, 24006888102075722880975, 15800133137207909144690421, 10580854797781352259168325347, 7186571606168294602440625922385, 4938826696886704892539811529645855
Offset: 0
-
g():= seq(convert(n, base, 2)[1..4], n=17..31):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$4]):
seq(a(n), n=0..16);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 4]], {n, 2^4 + 1, 2^5 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {4}]];
a /@ Range[0, 16] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263163
Number of lattice paths starting at {n}^5 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 31, 32461, 142090291, 944362553521, 7622403922836151, 68836844233002312181, 668865316589763487491811, 6842570537592835194176298241, 72725938463068824904583496062671, 796079042828286992045143086504942301, 8920612967950147759634381671622287341331
Offset: 0
-
g():= seq(convert(n, base, 2)[1..5], n=33..63):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$5]):
seq(a(n), n=0..12);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 5]], {n, 2^5 + 1, 2^6 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {5}]];
a /@ Range[0, 12] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263164
Number of lattice paths starting at {n}^6 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 63, 580693, 39991899123, 4727954015135121, 716137204351882049583, 125076804896889941384267749, 23963247580553153291287896467139, 4899254403362236213345570748744318209, 1051032705565051909388116876876306460192223
Offset: 0
-
g():= seq(convert(n, base, 2)[1..6], n=65..127):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$6]):
seq(a(n), n=0..10);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 6]], {n, 2^6 + 1, 2^7 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {6}]];
a /@ Range[0, 10] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263165
Number of lattice paths starting at {n}^7 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 127, 11917837, 15302345348179, 38074918201135688881, 127994492508527577494290807, 511210318493877135287739912958933, 2283244029676857615289372083169016508547, 11029283913008516141643899112236047179180872449
Offset: 0
-
g():= seq(convert(n, base, 2)[1..7], n=129..255):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$7]):
seq(a(n), n=0..9);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 7]], {n, 2^7 + 1, 2^8 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {7}]];
a /@ Range[0, 9] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263166
Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 255, 277284181, 7671206130046515, 463841686707958609540881, 39946850792952097272345707272335, 4211153593189257990239568354710957472133, 506051495006579137756029271328016744207715324419, 66656513992169790340795231563272399566454175106315563265
Offset: 0
-
g():= seq(convert(n, base, 2)[1..8], n=257..511):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$8]):
seq(a(n), n=0..8);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 8]], {n, 2^8 + 1, 2^9 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {8}]];
a /@ Range[0, 8] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263167
Number of lattice paths starting at {n}^9 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 511, 7229006221, 4888774762356549331, 8144781718207791515101819441, 20371729407721971932197861769050382551, 64254115995388375135778208276014009097192012661, 235485313707274694851291521951126742198585792399471283971
Offset: 0
-
g():= seq(convert(n, base, 2)[1..9], n=513..1023):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$9]):
seq(a(n), n=0..7);
-
g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 9]], {n, 2^9+1, 2^10-1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {9}]];
a /@ Range[0, 7] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)
A263168
Number of lattice paths starting at {n}^10 and ending when any component equals 0, using steps that decrement one or more components by one.
Original entry on oeis.org
1, 1023, 208994018773, 3864094036317649535283, 198305312034897003898098826655121, 16102861078300336871094550725929002523470383, 1698612808615154132767781717350125427082238529142835109, 212216707280526234296212923289763064481087995125148762713351022339
Offset: 0
-
g():= seq(convert(n, base, 2)[1..10], n=1025..2047):
b:= proc(l) option remember;
`if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
end:
a:= n-> b([n$10]):
seq(a(n), n=0..5);