login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179900 Triangle T(n,k) read by rows: coefficient of [x^k] of the polynomial p_n(x)=(5-x)*p_{n-1}(x)-p_{n-2}(x), p_0=1, p_1=5-x. 1
1, 5, -1, 24, -10, 1, 115, -73, 15, -1, 551, -470, 147, -20, 1, 2640, -2828, 1190, -246, 25, -1, 12649, -16310, 8631, -2400, 370, -30, 1, 60605, -91371, 58275, -20385, 4225, -519, 35, -1, 290376, -501150, 374115, -157800, 41140, -6790, 693, -40, 1, 1391275 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The row sums are 1, 4, 15, 56, 209, 780, 2911, .. A001353.
Apart from signs, the same as A123967.
This can also be defined as the coefficients of the characteristic polynomial of the n X n tridiagonal symmetric matrix with 5's on the diagonal and -1's on the two adjacent subdiagonals. Expansion of the determinant along the first column yields the recurrence of the definition.
LINKS
FORMULA
T(n,k) = 5*T(n-1,k)-T(n-1,k-1)-T(n-2,k) starting T(0,0)=1, T(1,0)=5 and T(1,1)=-1.
T(n,0) = A004254(n+1).
EXAMPLE
1 ; # 1
5, -1; # 5-x
24, -10, 1 ; # 24-10x+x^2
115, -73, 15, -1; # 115-73x+15x^2-x^3
551, -470, 147, -20, 1;
2640, -2828, 1190, -246, 25, -1;
12649, -16310, 8631, -2400, 370, -30, 1;
60605, -91371, 58275, -20385, 4225, -519, 35, -1;
290376, -501150, 374115, -157800, 41140, -6790, 693, -40, 1;
1391275, -2704755, 2313450, -1142730, 359275, -74571, 10220, -892, 45, -1;
MATHEMATICA
Clear[M, T, d, a, x, a0]
T[n_, m_, d_] := If[ n == m, 5, If[n == m - 1 || n == m + 1, -1, 0]]
M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]
Table[Det[M[d]], {d, 1, 10}]
Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]
a = Join[M[1], Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], { d, 1, 10}]]
Flatten[a]
MatrixForm[a]
CROSSREFS
Sequence in context: A201884 A294138 A207824 * A123967 A162259 A077195
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, Jul 31 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)