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A192815 Coefficient of x in the reduction of the polynomial (2*x + 1)^n by x^3 -> x^2 + x + 1. 3
0, 2, 4, 14, 72, 346, 1612, 7526, 35216, 164786, 770964, 3606974, 16875480, 78953226, 369388508, 1728211222, 8085563168, 37828901730, 176985297700, 828038725486, 3874040046440, 18124981139642, 84799056637292, 396738620092614 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
For discussions of polynomial reduction, see A192232 and A192744.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..100 from Vincenzo Librandi)
FORMULA
a(n) = 5*a(n-1) - 3*a(n-2) + 7*a(n-3).
a(n) = 2*A192816(n).
G.f.: 2*x*(1-3*x)/(1-5*x+3*x^2-7*x^3). - Bruno Berselli, Jul 11 2011
MATHEMATICA
(See A192814.)
LinearRecurrence[{5, -3, 7}, {0, 2, 4}, 30] (* G. C. Greubel, Jan 03 2019 *)
PROG
(PARI) concat([0], Vec(2*x*(1-3*x)/(1-5*x+3*x^2-7*x^3)+O(x^30))) \\ Charles R Greathouse IV, Jul 11 2011
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( 2*x*(1-3*x)/(1-5*x+3*x^2-7*x^3) )); // G. C. Greubel, Jan 03 2019
(Sage) (2*x*(1-3*x)/(1-5*x+3*x^2-7*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 03 2019
CROSSREFS
Sequence in context: A261002 A032147 A007712 * A075098 A340909 A052856
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 10 2011
STATUS
approved

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Last modified July 12 21:16 EDT 2024. Contains 374257 sequences. (Running on oeis4.)