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

0,4

Comments

Unsigned row sums appear to be A014739.

Links

Table of n, a(n) for n=0..90.

Example

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;
...

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 *)

Crossrefs

Sequence in context: A192812 A125127 A051120 * A260419 A117184 A035690

Adjacent sequences: A114473 A114474 A114475 * A114477 A114478 A114479

Keyword

sign,tabl,easy

Author

Gary W. Adamson, Nov 27 2006

Extensions

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

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

Status

approved