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A091573 Poincaré series [or Poincare series] of the preprojective algebra of an extended Dynkin diagram of type E_6. 7
7, 12, 17, 24, 31, 36, 41, 48, 55, 60, 65, 72, 79, 84, 89, 96, 103, 108, 113, 120, 127, 132, 137, 144, 151, 156, 161, 168, 175, 180, 185, 192, 199, 204, 209, 216, 223, 228, 233, 240, 247, 252, 257, 264, 271, 276, 281, 288, 295, 300, 305, 312, 319, 324, 329 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices of the AMS, Vol. 44, Number 5.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

FORMULA

a(n) = 6*n+6 (n odd), 6*n+7 (n==0 (mod 4)), 6*n+5 (n==2 (mod 4)).

G.f.: (7-2*x+7*x^2) / ((1+x^2)*(1-x)^2).

From Colin Barker, Oct 18 2015: (Start)

a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>3.

a(n) = (12+(-i)^n+i^n+12*n)/2 where i = sqrt(-1).

(End)

MATHEMATICA

CoefficientList[ Series[ (7 - 2x + 7x^2) / (1 - 2x + 2x^2 - 2x^3 + x^4), {x, 0, 49}], x] (* Jean-François Alcover, Dec 02 2011 *)

PROG

(PARI) a(n) = (12+(-I)^n+I^n+12*n)/2 \\ Colin Barker, Oct 18 2015

(PARI) Vec((7-2*x+7*x^2)/((1+x^2)*(1-x)^2) + O(x^100)) \\ Colin Barker, Oct 18 2015

(PARI) a(n) = if(n%2 == 1, 6*n+6, if(n%4 == 0, 6*n+7, 6*n+5));

vector(100, n, a(n-1)) \\ Altug Alkan, Oct 18 2015

CROSSREFS

Cf. A004525, A091571, A091572, A091574, A091575, A091576, A091577.

Sequence in context: A091576 A272733 A272741 * A183046 A272785 A272808

Adjacent sequences:  A091570 A091571 A091572 * A091574 A091575 A091576

KEYWORD

easy,nonn

AUTHOR

Paul Boddington, Jan 22 2004

EXTENSIONS

G.f. corrected by Colin Barker, Oct 18 2015

STATUS

approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)