A008644 - OEIS

A008644

Molien series of 5 X 5 upper triangular matrices over GF( 2 ).

1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 26, 36, 36, 46, 46, 60, 60, 74, 74, 94, 94, 114, 114, 140, 140, 166, 166, 201, 201, 236, 236, 280, 280, 324, 324, 380, 380, 436, 436, 504, 504, 572, 572, 656, 656, 740, 740, 840, 840, 940, 940, 1060, 1060, 1180, 1180, 1320, 1320, 1460, 1460, 1625

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OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1, 2, 4, 8, an 16. [Joerg Arndt, Jul 12 2013]

REFERENCES

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

LINKS

Table of n, a(n) for n=0..64.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 243

Index entries for Molien series

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

FORMULA

G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16)). [Joerg Arndt, Jul 12 2013]

MAPLE

1/(1-x)/(1-x^2)/(1-x^4)/(1-x^8)/(1-x^16)

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^4)(1-x^8)(1-x^16)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1}, {1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 26, 36, 36, 46, 46, 60, 60, 74, 74, 94, 94, 114, 114, 140, 140, 166}, 70] (* Harvey P. Dale, Oct 16 2021 *)

PROG

(PARI) a(n)=floor((n^4+62*n^3+1271*n^2+9610*n+31125+(n+1)*(2*n^2+91*n+1179)*(-1)^n)/24576+1/512*(-1)^(n\2)*(n\2+1)*(n\2+15)+1/32*(-1)^(n\4)*(n\4+1)*(n%4>1)) \\ Tani Akinari, Jul 12 2013

(PARI) Vec(1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)*(1-x^16))+O(x^66)) \\ Joerg Arndt, Jul 12 2013

CROSSREFS

Sequence in context: A023023 A184157 A008643 * A008645 A018819 A357454

Adjacent sequences: A008641 A008642 A008643 * A008645 A008646 A008647

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved