A110851 Weight enumerator of [64,63,2] Reed-Muller code RM(5,6).

1, 2016, 635376, 74974368, 4426165368, 151473214816, 3284214703056, 47855699958816, 488526937079580, 3601688791018080, 19619725782651120, 80347448443237920, 250649105469666120, 601557853127198688, 1118770292985239888, 1620288010530347424, 1832624140942590534

Offset

0,2

Links

Georg Fischer, Table of n, a(n) for n = 0..32

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Formula

a(n) = binomial(64, 2*n). - Georg Fischer, Jul 01 2021

Example

4426165368*x^8*y^56 + 1620288010530347424*x^30*y^34 + 47855699958816*x^14*y^50 + 601557853127198688*x^26*y^38 + 80347448443237920*x^22*y^42 + 19619725782651120*x^20*y^44 + 488526937079580*x^16*y^48 + 3601688791018080*x^46*y^18 + 19619725782651120*x^44*y^20 + y^64 + 1832624140942590534*x^32*y^32 + 1118770292985239888*x^36*y^28 + 80347448443237920*x^42*y^22 + 1118770292985239888*x^28*y^36 + 3601688791018080*x^18*y^46 + 2016*x^2*y^62 + 635376*x^60*y^4 + 74974368*x^58*y^6 + 74974368*x^6*y^58 + 635376*x^4*y^60 + 3284214703056*x^12*y^52 + 601557853127198688*x^38*y^26 + 1620288010530347424*x^34*y^30 + 151473214816*x^10*y^54 + 250649105469666120*x^24*y^40 + 3284214703056*x^52*y^12 + 47855699958816*x^50*y^14 + 488526937079580*x^48*y^16 + 250649105469666120*x^40*y^24 + x^64 + 151473214816*x^54*y^10 + 4426165368*x^56*y^8 + 2016*x^62*y^2

Maple

seq(binomial(64, 2*n), n=0..32); # Georg Fischer, Jul 01 2021

Mathematica

RecurrenceTable[{(2*n^2-n)*a[n]==(2*n^2-131*n+2145)*a[n-1], a[0]==1}, a[n], {n, 0, 33}] (* Georg Fischer, Jul 01 2021 *)

Crossrefs

Cf. A110829 (RM(2,3)), A110839 (RM(3,4)), A110847 (RM(4,5)), A110852 (32nd root).

Sequence in context: A166818 A166800 A223216 * A282331 A183768 A119517

Adjacent sequences: A110848 A110849 A110850 * A110852 A110853 A110854

Keyword

nonn,fini,full

Author

N. J. A. Sloane and Nadia Heninger Aug 18 2005

Status

approved