A154221 A simple Pascal-like triangle.

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, 33, 33, 33, 33, 1, 1, 65, 65, 65, 65, 65, 65, 65, 1, 1, 129, 129, 129, 129, 129, 129, 129, 129, 1, 1, 257, 257, 257, 257, 257, 257, 257, 257, 257, 1

Offset: 0

Author

Paul Barry, Jan 05 2009

Keywords

• easy
• nonn
• tabl

Comments

First column is A094373. Central coefficients are A123166.

Row sums are A154222. Diagonal sums are A154223.

Examples

			Triangle begins
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, 33, 33, 33, 33, 1,
1, 65, 65, 65, 65, 65, 65, 65, 1
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows

Programs

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

Maple

A154221 := proc(n,k)
    local f1,f2 ;
    f1 := 2^(k-1) ;
    if k = 0 then
        f1 := f1-1/2 ;
    end if;
    f2 := 2^(n-k-1) ;
    if n-k = 0 then
        f2 := f2-1/2 ;
    end if;
    1+f1*f2 ;
end proc:
seq(seq(A154221(n,k),k=0..n),n=0..10) ; # R. J. Mathar, Feb 05 2015

Mathematica

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 *)

Formula

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