

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 kth 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 kth 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^54*x^32*x^23*x1) / (2*x^94*x^62*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: A306443 A336518 A189073 * A196565 A104633 A102022
Adjacent sequences: A107268 A107269 A107270 * A107272 A107273 A107274


KEYWORD

nonn,easy


AUTHOR

Gary W. Adamson, May 15 2005


STATUS

approved



