OFFSET
1,2
COMMENTS
Sequence relating to finite differences.
Taking subsets (k = 1,2,3, ...) of three terms: [1, 3, 2; 6, 6, 2; 14, 24, 12; ...), 3 terms in the k-th subset are coefficients in a second degree equation f(x) such that the binomial transform of (k+1)-th subset = terms generated by f(x) of k-th subset. Example: Binomial transform of [14, 24, 12] = 14, 38, 74, 122, ...; f(x)= 6x^2 + 6x + 2. [14, 24, 12] = the 3rd subset of 3 terms, [6, 6, 2] = the second subset. Then, binomial transform of [6, 6, 2] = [6, 12, 20, 33, 42...] such that f(x) = x^2 + 3x + 2, where [1, 3, 2] is the second three term subset of A107271.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,4,0,0,-2).
FORMULA
G.f.: -x*(2*x^6+2*x^5-4*x^3-2*x^2-3*x-1) / (2*x^9-4*x^6-2*x^3+1). [Colin Barker, Dec 13 2012]
EXAMPLE
M^3 * [1 0 0] = [14, 24, 12].
MATHEMATICA
LinearRecurrence[{0, 0, 2, 0, 0, 4, 0, 0, -2}, {1, 3, 2, 6, 6, 2, 14, 24, 12}, 40] (* Harvey P. Dale, Jul 19 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, May 15 2005
STATUS
approved