OFFSET
0,2
LINKS
Wikipedia, E_7 (mathematics).
Index entries for linear recurrences with constant coefficients, signature (12,-54,112,-105,36,-1).
FORMULA
G.f.: -(2*x-1)*(x^4 - 12*x^3 + 19*x^2 - 8*x + 1) / (x^6 - 36*x^5 + 105*x^4 - 112*x^3 + 54*x^2 - 12*x + 1). - Colin Barker, May 25 2013
EXAMPLE
a(6) = 430 = leftmost term in M^6 * [1,0,0,0,0,0,0].
MAPLE
with(linalg): M[1]:=matrix(7, 7, [2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, -1, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, 0, 2]): for n from 2 to 30 do M[n]:=multiply(M[1], M[n-1]) od:1, seq(M[n][1, 1], n=1..30); # Emeric Deutsch, Jan 20 2007
PROG
(PARI) {a(n)=local(E7=[2, -1, 0, 0, 0, 0, 0; -1, 2, -1, 0, 0, 0, 0; 0, -1, 2, -1, 0, 0, -1; 0, 0, -1, 2, -1, 0, 0; 0, 0, 0, -1, 2, -1, 0; 0, 0, 0, 0, -1, 2, 0; 0, 0, -1, 0, 0, 0, 2]); (E7^n)[1, 1]} \\ Paul D. Hanna, Jan 02 2007
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 28 2006
EXTENSIONS
More terms from Paul D. Hanna, Jan 02 2007
STATUS
approved