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A107271 Let M = the 3 X 3 matrix [1 1 1; 3 1 0; 2 0 0]. Perform M^n * [1 0 0] getting (1, 3, 2; 6, 6, 2; 14, 24, 12; 50, 66, 28;...) which we string together to form the sequence. 1
1, 3, 2, 6, 6, 2, 14, 24, 12, 50, 66, 28, 144, 216, 100, 460, 648, 288, 1396, 2028, 920, 4344, 6216, 2792, 13352, 19248, 8688, 41288, 59304, 26704, 127296, 183168, 82576, 393040, 565056, 254592, 1212688, 1744176, 786080 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..39.

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

Sequence in context: A293549 A306443 A189073 * A196565 A104633 A102022

Adjacent sequences:  A107268 A107269 A107270 * A107272 A107273 A107274

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, May 15 2005

STATUS

approved

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Last modified February 22 16:36 EST 2020. Contains 332140 sequences. (Running on oeis4.)