

A231181


Expansion of 1/(1  x  4*x^2 + 3*x^3 + 3*x^4  x^5).


6



1, 1, 5, 6, 20, 27, 75, 110, 275, 429, 1001, 1637, 3639, 6172, 13243, 23104, 48280, 86090, 176341, 319792, 645150, 1185305, 2363596, 4386331, 8669142, 16212913, 31825005, 59873834, 116914020, 220964744, 429737220, 815057639, 1580244061
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OFFSET

0,3


COMMENTS

This sequence is fundamental for the coefficient sequences for the nonnegative powers of rho(11) = 2*cos(Pi/n) (length ration (smallest diagonal)/side in the regular 11gon (Hendecagon)) when written in the power basis of the degree 5 number field Q(rho(11)). See A187360 for the minimal polynomial of rho(11) which is C(11, x) = x^5  x^4  4*x^3 + 3*x^2 + 3*x  1. See A2311825 for these coefficient sequences.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..3532
Genki Shibukawa, New identities for some symmetric polynomials and their applications, arXiv:1907.00334 [math.CA], 2019.
Index entries for linear recurrences with constant coefficients, signature (1,4,3,3,1).


FORMULA

G.f.: 1/(1  x  4*x^2 + 3*x^3 + 3*x^4  x^5).
a(n) = a(n1) + 4*a(n2)  3*a(n3)  3*a(n4) + a(n5) for n>=0, with a(5)=1, a(4)=a(3)=a(2)=a(1)=0.


MATHEMATICA

CoefficientList[Series[1/(1x4x^2+3x^3+3x^4x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 4, 3, 3, 1}, {1, 1, 5, 6, 20}, 50] (* Harvey P. Dale, Nov 13 2013 *)


CROSSREFS

Cf. A231182, A231183, A231184, A231185.
Sequence in context: A317444 A072577 A231182 * A259775 A327860 A057520
Adjacent sequences: A231178 A231179 A231180 * A231182 A231183 A231184


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, Nov 05 2013


STATUS

approved



