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

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

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

Examples

			a(2) = 33280 is the number of inequivalent 4 X 4 binary matrices up to taking the transpose. - _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).

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).

Programs

GAP

List([0..20], n-> n^10*(n^6 +1)/2); # G. C. Greubel, Oct 11 2019

Magma

[n^10*(n^6+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 27 2011

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 *)

PARI

concat(0, Vec(-x*(x +1)*(x^14 +33262*x^13 [phone]*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 [phone]*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

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