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

0,5

Comments

First column is A094373. Central coefficients are A123166.

Row sums are A154222. Diagonal sums are A154223.

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A235803 A138201 A220614 * A026736 A230859 A213086

Adjacent sequences: A154218 A154219 A154220 * A154222 A154223 A154224

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 05 2009

Status

approved