Zerinvary Lajos - cp's OEIS frontend

A159038 a(n) = 8 * n!.

8, 16, 48, 192, 960, 5760, 40320, 322560, 2903040, 29030400, 319334400, 3832012800, 49816166400, 697426329600, 10461394944000, 167382319104000, 2845499424768000, 51218989645824000, 973160803270656000

Offset: 1

Zerinvary Lajos, Apr 03 2009

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.

Cf. A000142, A052560, A052578, A052648, A052849, A062098.

A159038 := proc(n)
    8*n! ;
end proc:
seq(A159038(n),n=1..10) ; # R. J. Mathar, Sep 30 2013

a(n) = 8 * A000142(n) for n > 0.

A167166 a(n) = n^7 mod 16.

Original entry on oeis.org

0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0, 5, 0, 15, 0, 1, 0, 11, 0, 13, 0, 7, 0, 9, 0, 3, 0

Offset: 0

Zerinvary Lajos, Oct 29 2009

Equivalently: n^(4*m+7) mod 16. - G. C. Greubel, Jun 04 2016

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Table[Mod[n^7, 16], {n, 0, 10}] (* G. C. Greubel, Jun 04 2016 *)
PowerMod[Range[0,100],7,16] (* or *) PadRight[{},100,{0,1,0,11,0,13,0,7,0,9,0,3,0,5,0,15}] (* Harvey P. Dale, Jul 29 2018 *)

a(n)=n^7%16 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,7,16)for n in range(0, 93)] #

From R. J. Mathar, Sep 30 2013: (Start)
a(n) = a(n-16).
G.f. -x*(1 +11*x^2 +13*x^4 +7*x^6 +9*x^8 +3*x^10 +5*x^12 +15*x^14) / ( (x-1)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8) ). (End)
a(n) = A130909(A001015(n)). - Michel Marcus, Jun 04 2016

A167420 2^n mod 14.

Original entry on oeis.org

1, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8, 2, 4, 8

Offset: 0

Zerinvary Lajos, Nov 03 2009

Index entries for linear recurrences with constant coefficients, signature (0,0,1).

PowerMod[2,Range[0,100],14] (* Harvey P. Dale, Jul 25 2011 *)

a(n)=lift(Mod(2,14)^n) \\ Charles R Greathouse IV, Mar 22 2016

[power_mod(2,n,14)for n in range(0,100)] #

G.f.: 1 + -2*x*(1+2*x+4*x^2) / ( (x-1)*(1+x+x^2) ). - R. J. Mathar, Jun 18 2019

A167421 2^n mod 22.

Original entry on oeis.org

1, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6, 12, 2, 4, 8, 16, 10, 20, 18, 14, 6

Offset: 0

Zerinvary Lajos, Nov 03 2009

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, -1, 1).

PowerMod[2,Range[0,80],22] (* Harvey P. Dale, Dec 11 2012 *)

a(n)=lift(Mod(2,22)^n) \\ Charles R Greathouse IV, Mar 22 2016

[power_mod(2,n,22)for n in range(0,84)] #

a(n)= +a(n-1) -a(n-5) +a(n-6), n>6. .G.f.: (x+2*x^2+4*x^3+8*x^4-5*x^5+11*x^6+1)/ ((1-x) * (1+x) * (x^4-x^3+x^2-x+1)). - R. J. Mathar, Apr 13 2010

A167527 n^5 mod 49.

Original entry on oeis.org

0, 1, 32, 47, 44, 38, 34, 0, 36, 4, 40, 37, 10, 20, 0, 22, 25, 33, 30, 31, 6, 0, 8, 46, 26, 23, 3, 41, 0, 43, 18, 19, 16, 24, 27, 0, 29, 39, 12, 9, 45, 13, 0, 15, 11, 5, 2, 17, 48, 0, 1, 32, 47, 44, 38, 34, 0, 36, 4, 40, 37, 10, 20, 0, 22, 25, 33, 30, 31, 6, 0, 8, 46, 26, 23, 3

Offset: 0

Zerinvary Lajos, Nov 05 2009

PowerMod[Range[0,80],5,49] (* Harvey P. Dale, Apr 10 2013 *)

a(n)=n^5%49 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,5,49)for n in range(0, 76)] #

A167545 n^6 mod 16.

Original entry on oeis.org

0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0, 1, 0, 9, 0, 9, 0, 1, 0

Offset: 0

Zerinvary Lajos, Nov 06 2009

PowerMod[Range[0,110],6,16] (* or *) With[{nn=15},PadRight[{},8nn,{0,1,0,9,0,9,0,1}]] (* Harvey P. Dale, Nov 10 2011 *)

a(n)=n^6%16 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,6,16)for n in range(0, 105)] #

A167628 n^11 mod 13.

Original entry on oeis.org

0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 0, 1, 7, 9

Offset: 0

Zerinvary Lajos, Nov 07 2009

Equivalently: n^(12*m+11) (mod 13). - G. C. Greubel, Jun 17 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

PowerMod[Range[0,100],11,13] (* Harvey P. Dale, Oct 31 2011 *)

a(n)=n^11%13 \\ Charles R Greathouse IV, Apr 06 2016

[power_mod(n,11,13) for n in range(0, 95)]

a(n+13) = a(n). - G. C. Greubel, Jun 17 2016

A172242 Number of 10-D hypercubes in an n-dimensional hypercube.

Original entry on oeis.org

1, 22, 264, 2288, 16016, 96096, 512512, 2489344, 11202048, 47297536, 189190144, 722362368, 2648662016, 9372188672, 32133218304, 107110727680, 348109864960, 1105760747520, 3440144547840, 10501493882880, 31504481648640

Offset: 10

Zerinvary Lajos, Jan 29 2010

With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly ten (10) u's.

Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (22,-220,1320,-5280,14784,-29568,42240,-42240,28160,-11264,2048).

Cf. A001788, A001789, A003472, A038207, A054849, A002409, A140325, A054851, A140354.

Table[Binomial[n + 10, 10]*2^n, {n, 0, 22}]

[lucas_number2(n, 2, 0)*binomial(n,10)/2^10 for n in range(10, 31)] # Zerinvary Lajos, Feb 05 2010

a(n) = A038207(n,10).
a(n) = binomial(n,10)*2^(n-10). [Corrected by R. J. Mathar, Feb 21 2010]
G.f.: -x^10/(2*x-1)^11. - Colin Barker, Nov 11 2012
a(n) = Sum_{i=10..n} binomial(i,10)*binomial(n,i). Example: for n=15, a(15) = 1*3003 + 11*1365 + 66*455 + 286*105 + 1001*15 + 3003*1 = 96096. - Bruno Berselli, Mar 23 2018
From Amiram Eldar, Jan 07 2022: (Start)
Sum_{n>=10} 1/a(n) = 1879/126 - 20*log(2).
Sum_{n>=10} (-1)^n/a(n) = 393660*log(3/2) - 20111419/126. (End)

A159083 Products of 7 consecutive integers.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 5040, 40320, 181440, 604800, 1663200, 3991680, 8648640, 17297280, 32432400, 57657600, 98017920, 160392960, 253955520, 390700800, 586051200, 859541760, 1235591280, 1744364160, 2422728000, 3315312000, 4475671200, 5967561600, 7866331200

Offset: 0

Zerinvary Lajos, Apr 05 2009

Michael De Vlieger and Harvey P. Dale, Table of n, a(n) for n = 0..10000 (first 1000 terms by Harvey P. Dale.)
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A052762, A052787, A053625, A173333.

Equals A008279(n,7) (for n>=7).

I:=[0,0,0,0,0,0,0,5040]; [n le 8 select I[n] else 8*Self(n-1) - 28*Self(n-2) +56*Self(n-3) -70*Self(n-4) +56*Self(n-5) -28*Self(n-6) +8*Self(n-7) -Self(n-8): n in [1..30]]; // G. C. Greubel, Jun 28 2018

G(x):=x^7*exp(x): f[0]:=G(x): for n from 1 to 36 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..33);

Table[Times@@(n+Range[0,6]),{n,-6,25}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,0,0,0,0,0,0,5040},30] (* Harvey P. Dale, Apr 07 2018 *)

my(x='x+O('x^30)); concat([0,0,0,0,0,0,0], Vec(5040*x^7/(1-x)^8)) \\ G. C. Greubel, Jun 28 2018

E.g.f.: x^7*exp(x).
For n>=8: a(n) = A173333(n,n-7). - Reinhard Zumkeller, Feb 19 2010
G.f.: 5040*x^7/(1-x)^8. - Colin Barker, Mar 27 2012
From Amiram Eldar, Mar 08 2022: (Start)
a(n) = n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6) = n!/(n-7)!.
Sum_{n>=7} 1/a(n) = 1/4320.
Sum_{n>=7} (-1)^(n+1)/a(n) = 4*log(2)/45 - 1327/21600. (End)

A172978 a(n) = binomial(n+10, 10)*4^n.

Original entry on oeis.org

1, 44, 1056, 18304, 256256, 3075072, 32800768, 318636032, 2867724288, 24216338432, 193730707456, 1479398129664, 10848919617536, 76776969601024, 526470648692736, 3509804324618240, 22813728110018560, 144934272698941440, 901813252348968960, 5505807224867389440

Offset: 0

Zerinvary Lajos, Feb 06 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..157
Index entries for linear recurrences with constant coefficients, signature (44,-880,10560,-84480,473088,-1892352,5406720,-10813440,14417920,-11534336,4194304).

Cf. A002697, A038845, A038846, A040075, A045543, A054337, A054338, A054339, A054340

[Binomial(n+10, 10)*4^n: n in [0..30]]; // Vincenzo Librandi, Jun 06 2011

Table[Binomial[n + 10, 10]*4^n, {n, 0, 20}]

From Amiram Eldar, Mar 27 2022: (Start)
G.f.: 1/(1 - 4*x)^11.
Sum_{n>=0} 1/a(n) = 14269429/63 - 787320*log(4/3).
Sum_{n>=0} (-1)^n/a(n) = 78125000*log(5/4) - 1098284605/63. (End)

cp's OEIS Frontend

User: Zerinvary Lajos

A159038 a(n) = 8 * n!.

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A167166 a(n) = n^7 mod 16.

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A167420 2^n mod 14.

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A167421 2^n mod 22.

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A167527 n^5 mod 49.

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A167545 n^6 mod 16.

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A167628 n^11 mod 13.

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A172242 Number of 10-D hypercubes in an n-dimensional hypercube.

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Sage

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