A114476 Triangle read by rows: inverse of triangle in A061554 with signs in each column +,+,-,-,+,+,-,-,...

1, -1, 1, 3, -1, 1, -3, 4, -1, 1, 5, -4, 5, -1, 1, -5, 9, -5, 6, -1, 1, 7, -9, 14, -6, 7, -1, 1, -7, 16, -14, 20, -7, 8, -1, 1, 9, -16, 30, -20, 27, -8, 9, -1, 1, -9, 25, -30, 50, -27, 35, -9, 10, -1, 1, 11, -25, 55, -50, 77, -35, 44, -10, 11, -1, 1, -11, 36, -55, 105, -77, 112, -44, 54, -11, 12, -1, 1, 13, -36, 91, -105, 182, -112, 156, -54, 65, -12, 13, -1, 1

Offset: 0

Author

Gary W. Adamson, Nov 27 2006

Keywords

• sign
• tabl
• easy

Comments

Unsigned row sums appear to be A014739.

Examples

			Start with a signed version of A061554:
1;
1, 1;
-2, 1, 1;
-3, -3, 1, 1;
6, -4, -4, 1, 1;
10, 10, -5, -5, 1;
...
and invert it, getting:
1
-1, 1;
3, -1, 1;
-3, 4, -1, 1;
5, -4, 5, -1, 1;
-5, 9, -5, 6, -1, 1;
...
		

Programs

Maple

A061554 := proc(n,k) binomial(n+k,floor(k/2)) ; end: nmax := 13 : A := array(1..nmax,1..nmax) : for r from 1 to nmax do for c from 1 to nmax do A[r,c] := A061554(c-1,r-c)*(-1)^floor((r-c)/2) ; od: od: A := linalg[inverse](A) : for r from 1 to nmax do for c from 1 to r do printf("%d, ", A[r,c]) ; od: od: # R. J. Mathar, Jan 31 2008

Mathematica

A061554[n_, k_] := Binomial[n+k, Floor[k/2]];
nmax = 13;
A = Table[A061554[c-1, r-c]*(-1)^Floor[(r-c)/2], {r, nmax}, {c, nmax}];
A = Inverse[A];
Table[A[[r, c]], {r, nmax}, {c, r}] // Flatten (* Jean-François Alcover, May 01 2023 *)

Extensions

Edited by N. J. A. Sloane, Dec 01 2006

More terms from R. J. Mathar, Jan 31 2008