A370888
a(n) = (n-1)*(2*(n-2)!+1).
Original entry on oeis.org
3, 6, 15, 52, 245, 1446, 10087, 80648, 725769, 7257610, 79833611, 958003212, 12454041613, 174356582414, 2615348736015, 41845579776016, 711374856192017, 12804747411456018, 243290200817664019, 4865804016353280020, 102181884343418880021, 2248001455555215360022, 51704033477769953280023, 1240896803466478878720024
Offset: 2
- Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
- Michael De Vlieger, Table of n, a(n) for n = 2..450
- Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 9.
A371217
The maximum deck size to perform Colm Mulcahy's n-card trick.
Original entry on oeis.org
1, 4, 15, 52, 197, 896, 4987, 33216, 257161, 2262124, 22241671, 241476060, 2867551117, 36960108680, 513753523571, 7659705147976, 121918431264273, 2063255678027668, 36991535865656959, 700377953116334788, 13963866589144933461, 292421219327021540176, 6417047546280200867819
Offset: 1
Suppose the deck consists of 4 cards (1,2,3,4), and the assistant gets two cards. If the two cards contain 4, the assistant hides 4 and signals it with the other card face down. If there is no 4, then the cards are a and a+1 modulo 3. The assistant hides a+1, and signals it with a.
- Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
- Colm Mulcahy, Mathematical card magic: fifty-two new effects, published by CRC press, 2013.
- Alois P. Heinz, Table of n, a(n) for n = 1..450
- Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 10.
-
a:= proc(n) option remember; `if`(n<4, n*(n^2-2*n+2),
((11*n^2-66*n-61)*a(n-1) -(17*n^2-155*n+134)*a(n-2)
+(n-3)*(n-81)*a(n-3) +(n-4)*(5*n+26)*a(n-4))/(11*n-72))
end:
seq(a(n), n=1..23); # Alois P. Heinz, Mar 18 2024
-
Table[1 + (k - 1)(2 Sum[Binomial[k - 1, i] (i - 1)!, {i, 1, k - 1}] + 1), {k, 20}]
-
from math import factorial
def A371217(n): return n+((n-1)*sum(factorial(n-1)//((i+1)*factorial(n-i-2)) for i in range(n-1))<<1) # Chai Wah Wu, May 02 2024
A054119
a(n) = n! + (n-1)! + (n-2)!.
Original entry on oeis.org
1, 2, 4, 9, 32, 150, 864, 5880, 46080, 408240, 4032000, 43908480, 522547200, 6745939200, 93884313600, 1401079680000, 22317642547200, 377917892352000, 6778983923712000, 128403161542656000, 2560949482291200000, 53645489280294912000, 1177524571957493760000, 27027108408834293760000
Offset: 0
Equals T(n, 3), array T as in
A054115.
Row 6 of
A276955 (from a(3)=9 onward).
-
[1,2] cat [Factorial(n)+Factorial(n-1)+Factorial(n-2): n in [2..20]]; // Vincenzo Librandi, Oct 05 2011
-
f:= n-> `if`(n<0, 0, n!):
seq(f(n)+f(n-1)+f(n-2), n=0..23);
-
Join[{1,2},Table[n!+(n+1)!+(n+2)!,{n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
Join[{1,2,4},Plus@@@Partition[Range[30]!,3,1]] (* Harvey P. Dale, Aug 29 2024 *)
-
f(n) = if (n<0, 0, n!);
a(n) = f(n) + f(n-1) + f(n-2); \\ Michel Marcus, Sep 20 2022
-
(define (A054119 n) (if (<= n 1) (+ 1 n) (+ (A000142 n) (A000142 (- n 1)) (A000142 (- n 2))))) ;; Antti Karttunen, Sep 24 2016
A108217
a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.
Original entry on oeis.org
1, 1, 3, 7, 26, 126, 744, 5160, 41040, 367920, 3669120, 40279680, 482630400, 6266937600, 87657292800, 1313901388800, 21009968179200, 356995102464000, 6423296495616000, 122000787836928000, 2439304381882368000, 51212587272118272000, 1126433629785784320000
Offset: 0
Miklos Kristof, following a suggestion from Peter Boros, (borospet(AT)freemail.hu), Jun 16 2005
a(6) = 6!+4! = 720+24 = 744.
Row 5 of
A276955, from term a(3)=7 onward.
-
a:= n-> `if`(n<2, 1, n!+(n-2)!):
seq(a(n), n=0..30);
-
Table[If[n<2,1,n!+(n-2)!],{n,0,30}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
Join[{1,1},#[[1]]+#[[3]]&/@Partition[Range[0,20]!,3,1]] (* Harvey P. Dale, Nov 19 2015 *)
-
(define (A108217 n) (if (<= n 1) 1 (* (A002061 n) (A000142 (- n 2))))) ;; Antti Karttunen, Sep 23 2016
A351580
a(n) is the number of multisets of size n-1 consisting of permutations of n elements.
Original entry on oeis.org
1, 2, 21, 2600, 9078630, 1634935320144, 22831938997720867560, 34390564970975286088924022400, 7457911916650283082000186530740981347120, 300682790088737748950725540713718365319268411170195200, 2830053444386286847574443631356044745870287426798365860653876609636480
Offset: 1
Starting with the following men's ranking table of order 3, where row k represents man k's rankings, the 1 in the 2nd position of row 3 means that man #3 ranks woman #2 as his 1st choice.
213
321
213
Step 1: reorder columns so row 1 is in natural order:
123
231
123
Step 2: reorder rows 2 to n so rows are in lexical order:
123
123
231
a(3)=21 because there are 1+2+3+4+5+6 = 21 possibilities for the last two rows in lexical order, with 3!=6 possible permutations for each row.
The 21 tables for a(3) are the following:
123 123 123 123 123 123 123
123 123 123 123 123 123 132
123 132 213 231 312 321 132
.
123 123 123 123 123 123 123
132 132 132 132 213 213 213
213 231 312 321 213 231 312
.
123 123 123 123 123 123 123
213 231 231 231 312 312 321
321 231 312 321 312 321 321
Showing 1-5 of 5 results.
Comments