A170798 a(n) = n^10*(n^6 + 1)/2.

0, 1, 33280, 21552885, 2148007936, 76298828125, 1410585186816, 16616606522425, 140738025226240, 926511837818121, 5000005000000000, 22974877900498381, 92442160406200320, 332708373520835845, 1088976813532013056

Offset

0,3

Comments

a(n) is number of distinct 4 X 4 matrices with entries in {1,2,...,n} when a matrix and its transpose are considered equivalent. - David Nacin, Feb 20 2017

Cycle index of this S2 group action is (s(2)^6s(1)^4+s(1)^16)/2. - David Nacin, Feb 20 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Formula

G.f.: x*(x+1)*(x^14 + 33262*x^13 + 20953999*x^12 + 1765180292*x^11 + 40926077261*x^10 + 350131349138*x^9 + 1253612167971*x^8 + 1937785948152*x^7 + 1253612167971*x^6 + 350131349138*x^5 + 40926077261*x^4 + 1765180292*x^3 + 20953999*x^2 + 33262*x + 1)/(1-x)^17. - Colin Barker, Jul 11 2015

E.g.f.: x*(2 + 33278*x + 7151016*x^2 + 171833006*x^3 + 1096233075*x^4 + 2734949385*x^5 + 3281888484*x^6 + 2141764803*x^7 + 820784295*x^8 + 193754991*x^9 + 28936908*x^10 + 2757118*x^11 + 165620*x^12 + 6020*x^13 + 120*x^14 + x^15)*exp(x)/2. - G. C. Greubel, Oct 12 2019

Example

a(2) = 33280 is the number of inequivalent 4 X 4 binary matrices up to taking the transpose. - David Nacin, Feb 20 2017

Maple

seq(n^10*(n^6+1)/2, n=0..20); # G. C. Greubel, Oct 12 2019

Mathematica

Table[n^10*(n^6+1)/2, {n, 0, 30}] (* Harvey P. Dale, Aug 27 2016 *)

Prog

(Magma) [n^10*(n^6+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011
(PARI) concat(0, Vec(-x*(x +1)*(x^14 +33262*x^13 +20953999*x^12 +1765180292*x^11 +40926077261*x^10 +350131349138*x^9 +1253612167971*x^8 +1937785948152*x^7 +1253612167971*x^6 +350131349138*x^5 +40926077261*x^4 +1765180292*x^3 +20953999*x^2 +33262*x +1) / (x -1)^17 + O(x^30))) \\ Colin Barker, Jul 11 2015
(PARI) vector(21, m, (m-1)^10*((m-1)^6 + 1)/2) \\ G. C. Greubel, Oct 11 2019
(Sage) [n^10*(n^6 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019
(GAP) List([0..20], n-> n^10*(n^6 +1)/2); # G. C. Greubel, Oct 11 2019

Crossrefs

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), A170797 (m=5), this sequence (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

Sequence in context: A031660 A252291 A203619 * A043628 A205410 A337953

Adjacent sequences: A170795 A170796 A170797 * A170799 A170800 A170801

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Status

approved