0,5

Or, triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n tridiagonal matrix with 1's on the main, sub- and superdiagonal (0<=k<=n). The characteristic polynomial has a root 1+2cos(Pi/(n+1)). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 19 2006

Row sums have g.f. 1/(1+x^2); diagonal sums are (-1)^n. Riordan array (1/(1+x+x^2), x/(1+x+x^2)).

Apart from signs, identical to A101950.

Or, triangle read by rows in which row n gives coefficients of characteristic polynomial of tridaigonal matrix with 1's on the main diagonal and -1's on the two adjacent diagonals. For example: M(3)={{1, -1, 0}, {-1, 1, -1}, {0, -1, 1}}. - from More terms from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 15 2008

Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 256.

Number triangle T(n, k)=sum{j=0..n, (-1)^(k-j)*(-1)^((n-j)/2) C((n+j)/2, j)(1+(-1)^(n+j))C(j, k)/2}

Triangle starts:

1;

-1,1;

0,-2,1;

1,1,-3,1;

-1,2,3,-4,1;

0,-4,2,6,-5,1;

with(linalg): m:=proc(i, j) if abs(i-j)<=1 then 1 else 0 fi end: T:=(n, k)->coeff(charpoly(matrix(n, n, m), x), x, k): 1; for n from 1 to 12 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

a0[n_] := 1; b[n_] := -1; T[n_, m_, d_] := If[ n == m, a0[n], If[n == m - 1 || n == m + 1, If[n == m - 1, b[m - 1], If[n == m + 1, b[n - 1], 0]], 0]]; MO[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[ MO[n], x], x], {n, 1, 10}]]; Flatten[a] - from More terms from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 15 2008

Cf. A125090, A101950.

Sequence in context: A135222 A124094 A101950 this_sequence A164306 A111603 A136178

Adjacent sequences: A104559 A104560 A104561 this_sequence A104563 A104564 A104565

easy,sign,tabl

Paul Barry (pbarry(AT)wit.ie), Mar 15 2005

Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 10 2008