A144451 Triangle A(n,k) read by rows: A(n,1)=A(n,n)=1 and A(n,k) = A(n-2,k-1) - 2*A(n,k-1) + 1 for 1<k<n.

1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, -3, 8, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, -4, 17, -32, 1

Offset

1,9

Comments

Row sums are 1, 2, 2, 4, 3, 4, 4, 10, 5, -14, 6, 128, 7, -720, 8, 4630, 9, -30194, 10, ...

Links

Table of n, a(n) for n=1..55.

Formula

A(n,k) = A(n-2,k-1) - 2*A(n,k-1) + 1.

Example

1;
1, 1;
1, 0, 1;
1, 0, 2, 1;
1, 0, 1, 0, 1;
1, 0, 1, 1, 0, 1;
1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 2, -3, 8, 1;
1, 0, 1, 0, 1, 0, 1, 0, 1;
1, 0, 1, 0, 1, 1, -4, 17, -32, 1;

Maple

A144451 := proc(n, k)
    option remember;
    if k < 1 or k > n then
        0 ;
    elif n = 1 or n=k then
        1;
    else
        procname(n-2, k-1)-2*procname(n, k-1)+1 ;
    end if;
end proc: # R. J. Mathar, Jul 21 2015

Mathematica

A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := A[n, k] = A[n - 2, k - 1] - 2*A[n, k - 1] + 1; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]

Crossrefs

Sequence in context: A133300 A337101 A178779 * A259287 A342592 A090464

Adjacent sequences: A144448 A144449 A144450 * A144452 A144453 A144454

Keyword

tabl,sign,easy

Author

Roger L. Bagula and Gary W. Adamson, Oct 06 2008

Status

approved