Original entry on oeis.org
1, 1, 1, 1, -3, 1, 1, 17, 17, 1, 1, -239, -219, -239, 1, 1, 7169, 6933, 6933, 7169, 1, 1, -444479, -437307, -437563, -437307, -444479, 1, 1, 56004353, 55559877, 55567029, 55567029, 55559877, 56004353, 1, 1, -14225105663, -14169101307, -14169545803, -14169538395, -14169545803, -14169101307, -14225105663, 1
Offset: 0
Triangle begins as:
1;
1, 1;
1, -3, 1;
1, 17, 17, 1;
1, -239, -219, -239, 1;
1, 7169, 6933, 6933, 7169, 1;
1, -444479, -437307, -437563, -437307, -444479, 1;
-
b:= function(n,q)
if n=0 then return 0;
else return 1 - (q^n-1)*b(n-1,q);
fi; end;
T:= function(n,k,q) return 1 + b(n,q) - b(n-k,q) - b(k,q); end;
Flat(List([0..10], n-> List([0..n], k-> T(n,k,2) ))); # G. C. Greubel, Dec 07 2019
-
function b(n,q)
if n eq 0 then return 0;
else return 1 - (q^n-1)*b(n-1,q);
end if; return b; end function;
function T(n,k,q) return 1 + b(n,q) - b(n-k,q) - b(k,q); end function;
[ T(n,k,2) : k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 07 2019
-
A176339 := proc(n,m)
1-A176337(m)-A176337(n-m)+A176337(n) ;
end proc: # R. J. Mathar, May 04 2013
-
b[n_, q_]:= b[n, q]= If[n==0, 0, (1-q^n)*b[n-1, q] +1];
T[n_,k_,q_]:= 1 + b[n,q] -b[n-k,q] - b[k,q];
Table[T[n,k,2], {n,0,10}, {k,0,n}]//Flatten (* modified by G. C. Greubel, Dec 07 2019 *)
-
b(n,q) = if(n==0, 0, 1 + (1-q^n)*b(n-1,q) );
T(n,k,q) = 1 + b(n,q) - b(n-k,q) - b(k,q);
for(n=0,10, for(k=0,n, print1(T(n,k,2), ", "))) \\ G. C. Greubel, Dec 07 2019
-
@CachedFunction
def b(n, q):
if (n==0): return 0
else: return 1 - (q^n-1)*b(n-1,q)
def T(n,k,q): return 1 + b(n,q) - b(n-k,q) - b(k,q)
[[T(n,k,2) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 07 2019
A176338
a(n) = 1 + (1-3^n)*a(n-1) for n >=1, a(0) = 0.
Original entry on oeis.org
0, 1, -7, 183, -14639, 3542639, -2579041191, 5637784043527, -36983863325537119, 727916397973221576159, -42982007467522787629036631, 7614090694841791737333323035127, -4046432358866721800888421193787892879
Offset: 0
-
a:= function(n,q)
if n=0 then return 0;
else return 1 - (q^n-1)*a(n-1,q);
fi; end; List([0..15], n-> a(n,3) ); # G. C. Greubel, Dec 07 2019
-
function a(n,q)
if n eq 0 then return 0;
else return 1 - (q^n-1)*a(n-1,q);
end if; return a; end function;
[a(n,3): n in [0..15]]; // G. C. Greubel, Dec 07 2019
-
A176338 := proc(n)
if n = 0 then
0;
else
1+(1-3^n)*procname(n-1) ;
end if;
end proc: # R. J. Mathar, May 04 2013
-
a[n_, q_]:= a[n, q]= If[n==0, 0, (1-q^n)*a[n-1, q] +1]; Table[a[n, 3], {n,0,15}]
nxt[{n_,a_}]:={n+1,a(1-3^(n+1))+1}; NestList[nxt,{0,0},20][[;;,2]] (* Harvey P. Dale, Dec 31 2024 *)
-
q=3; a(n,q) = if(n==0, 0, 1 -(q^n-1)*a(n-1,q) );
vector(16, n, a(n-1,3)) \\ G. C. Greubel, Dec 07 2019
-
def a(n, q):
if (n==0): return 0
else: return 1 - (q^n-1)*a(n-1,q)
[a(n,3) for n in (0..15)] # G. C. Greubel, Dec 07 2019
Original entry on oeis.org
1, 1, 1, 1, -8, 1, 1, 190, 190, 1, 1, -14822, -14624, -14822, 1, 1, 3557278, 3542464, 3542464, 3557278, 1, 1, -2582583830, -2579026544, -2579041556, -2579026544, -2582583830, 1, 1, 5640363084718, 5637780500896, 5637784057984, 5637784057984, 5637780500896, 5640363084718, 1
Offset: 0
Triangle starts as:
1;
1, 1;
1, -8, 1;
1, 190, 190, 1;
1, -14822, -14624, -14822, 1;
1, 3557278, 3542464, 3542464, 3557278, 1;
-
b:= function(n,q)
if n=0 then return 0;
else return 1 - (q^n-1)*b(n-1,q);
fi; end;
T:= function(n,k,q) return 1 + b(n,q) - b(n-k,q) - b(k,q); end;
Flat(List([0..10], n-> List([0..n], k-> T(n,k,3) ))); # G. C. Greubel, Dec 07 2019
-
function b(n,q)
if n eq 0 then return 0;
else return 1 - (q^n-1)*b(n-1,q);
end if; return b; end function;
function T(n,k,q) return 1 + b(n,q) - b(n-k,q) - b(k,q); end function;
[ T(n,k,3) : k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 07 2019
-
b[n_, q_]:= b[n, q]= If[n==0, 0, (1-q^n)*b[n-1, q] +1];
T[n_,k_,q_]:= 1 + b[n,q] -b[n-k,q] - b[k,q];
Table[T[n,k,3], {n,0,10}, {k,0,n}]//Flatten (* modified by G. C. Greubel, Dec 07 2019 *)
-
b(n,q) = if(n==0, 0, 1 + (1-q^n)*b(n-1,q) );
T(n,k,q) = 1 + b(n,q) - b(n-k,q) - b(k,q);
for(n=0,10, for(k=0,n, print1(T(n,k,3), ", "))) \\ G. C. Greubel, Dec 07 2019
-
@CachedFunction
def b(n, q):
if (n==0): return 0
else: return 1 - (q^n-1)*b(n-1,q)
def T(n,k,q): return 1 + b(n,q) - b(n-k,q) - b(k,q)
[[T(n,k,3) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 07 2019
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