A154221 - OEIS

%I #13 Sep 08 2022 08:45:40

%S 1,1,1,1,2,1,1,3,3,1,1,5,5,5,1,1,9,9,9,9,1,1,17,17,17,17,17,1,1,33,33,

%T 33,33,33,33,1,1,65,65,65,65,65,65,65,1,1,129,129,129,129,129,129,129,

%U 129,1,1,257,257,257,257,257,257,257,257,257,1

%N A simple Pascal-like triangle.

%C First column is A094373. Central coefficients are A123166.

%C Row sums are A154222. Diagonal sums are A154223.

%H G. C. Greubel, <a href="/A154221/b154221.txt">Table of n, a(n) for the first 50 rows</a>

%F T(n,k)= 1 + (2^(k-1)-0^k/2)*(2^(n-k-1)-0^(n-k)/2).

%e Triangle begins

%e 1,

%e 1, 1,

%e 1, 2, 1,

%e 1, 3, 3, 1,

%e 1, 5, 5, 5, 1,

%e 1, 9, 9, 9, 9, 1,

%e 1, 17, 17, 17, 17, 17, 1,

%e 1, 33, 33, 33, 33, 33, 33, 1,

%e 1, 65, 65, 65, 65, 65, 65, 65, 1

%p A154221 := proc(n,k)

%p     local f1,f2 ;

%p     f1 := 2^(k-1) ;

%p     if k = 0 then

%p         f1 := f1-1/2 ;

%p     end if;

%p     f2 := 2^(n-k-1) ;

%p     if n-k = 0 then

%p         f2 := f2-1/2 ;

%p     end if;

%p     1+f1*f2 ;

%p end proc:

%p seq(seq(A154221(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Feb 05 2015

%t f[n_, k_] := 1 + (1/4)*(2^(k) - 0^k)*(2^(n - k) - 0^(n - k)); Table[f[n, i], {n, 0, 49}, {i, 0, n}] // Flatten (* _G. C. Greubel_, Sep 06 2016 *)

%o (Magma) /* As triangle */ [[1+(2^(k-1)-0^k/2)*(2^(n-k-1)-0^(n-k)/2): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Sep 06 2016

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Jan 05 2009