A346374
a(n) = f(n,n) where f(0,n) = f(n,0) = n! and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).
Original entry on oeis.org
1, 3, 15, 85, 511, 3221, 21339, 149969, 1133215, 9343525, 85089883, 860979329, 9665236335, 119534610885, 1613648163963, 23564301925713, 369437215969599, 6180713141601765, 109812899448776475, 2063836219057694753, 40894619124091715983, 851891564231714448133
Offset: 0
-
b:= proc(x, y) option remember; `if`(x=0, y!,
b(x-1, y)+b(sort([x, y-1])[])+b(x-1, y-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..26); # Alois P. Heinz, Jul 14 2021
-
F[0, 0] = 1; F[m_, 0] := m!; F[0, n_] := n!;
F[m_, n_] := F[m, n] = F[m - 1 , n ] + F[m , n - 1] + F[m - 1, n - 1];
Table[F[n, n], {n, 0, 100}]
A369580
a(n) := f(n, n), where f(0,0) = 1/3, f(0,k) = 0 and f(k,0) = 3^(k-1) if k > 0, and f(n, m) = f(n, m-1) + f(n-1, m) + 3*f(n-1, m-1) otherwise.
Original entry on oeis.org
2, 16, 138, 1216, 10802, 96336, 861114, 7708416, 69072354, 619380496, 5557080938, 49879087296, 447852531986, 4022246329936, 36132550233498, 324645166734336, 2917340834679234, 26219438520320016, 235672871308226634, 2118552629658530496, 19046140604787232242, 171241206828437556816
Offset: 1
-
def lis(n):
table = [[0]*(n+1) for _ in range(n+1)]
table[1][1] = 2
for i in range(1, n+1) :
table[i][0] = 3**(i-1)
for i in range(1, n+1) :
for j in range(1, n+1) :
if (i == 1 and j == 1) :
continue
table[i][j] = table[i][j-1] + table[i-1][j] + 3*table[i-1][j-1]
return [int(table[i][i]) for i in range(1, n+1)]
A346385
a(n) = f(n,n) where f(0,n) = f(n,0) = n^n and f(m,n) = f(m-1,n) + f(m,n-1) + f(m-1,n-1).
Original entry on oeis.org
1, 3, 19, 151, 1439, 16651, 234651, 3966271, 78504063, 1778555587, 45302809003, 1279960719335, 39697452556959, 1340332692660027, 48929424425580219, 1920103548827941263, 80597817202971009535, 3603262730476776975731, 170923354522784683176267
Offset: 0
-
F[0, 0] = 1; F[m_, 0] := m!; F[0, n_] := n^n;
F[m_, n_] := F[m, n] = F[m - 1 , n ] + F[m , n - 1] + F[m - 1, n - 1];
Table[F[n, n], {n, 0, 100}]
A350519
a(n) = A(n,n) where A(1,n) = A(n,1) = prime(n+1) and A(m,n) = A(m-1,n) + A(m,n-1) + A(m-1,n-1) for m > 1 and n > 1.
Original entry on oeis.org
3, 13, 63, 325, 1719, 9237, 50199, 275149, 1518263, 8422961, 46935819, 262512929, 1472854451, 8285893713, 46723439019, 264009961733, 1494486641911, 8473508472009, 48112827862527, 273541139290857, 1557023508876891, 8872219429659729, 50605041681538595, 288897992799897481
Offset: 1
The two-dimensional recurrence A(m,n) can be depicted in matrix form as
3 5 7 11 13 17 19 ...
5 13 25 43 67 97 133 ...
7 25 63 131 241 405 635 ...
11 43 131 325 697 1343 2383 ...
13 67 241 697 1719 3759 7485 ...
17 97 405 1343 3759 9237 20481 ...
19 133 635 2383 7485 20481 50199 ...
...
and then a(n) is the main diagonal of this matrix, A(n,n).
-
clear all
close all
sz = 14
f = zeros(sz,sz);
pp = primes(50);
f(1,:) = pp(2:end);
f(:,1) = pp(2:end);
for m=2:sz
for n=2:sz
f(m,n) = f(m-1,n-1)+f(m,n-1)+f(m-1,n);
end
end
an = []
for n=1:sz
an = [an f(n,n)];
end
S = sprintf('%i,',an);
S = S(1:end-1)
-
f[1,1]=3;f[m_,1]:=Prime[m+1];f[1,n_]:=Prime[n+1];f[m_,n_]:=f[m,n]=f[m-1,n]+f[m,n-1]+f[m-1,n-1];Table[f[n,n],{n,25}] (* Giorgos Kalogeropoulos, Jan 03 2022 *)
Showing 1-4 of 4 results.
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