A006095 -id:A006095 - cp's OEIS frontend

A075113 a(n) = A000217(n) - A048702(n).

0, 0, 0, 1, -1, 0, 4, 7, -7, -6, 0, 3, 13, 18, 28, 35, -35, -34, -24, -21, -5, 0, 14, 21, 43, 52, 70, 81, 105, 118, 140, 155, -155, -154, -136, -133, -105, -100, -78, -71, -35, -26, 0, 11, 47, 60, 90, 105, 151, 168, 202, 221, 265, 286, 324, 347, 399, 424, 466, 493, 545, 574, 620, 651, -651, -650, -616, -613, -561

Offset: 0

Antti Karttunen, Sep 02 2002

sign

The positions of the zeros seem to be given by A000975.

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A000217, A048701, A048702.

Cf. A000975, A000225, A006095.

A048702 := Join[{0}, Reap[For[k = 1, k < 1500, k += 2, bb = IntegerDigits[k, 2]; If[bb == Reverse[bb], If[EvenQ[Length[bb]], Sow[k/3]]]]][[2, 1]]]; Table[n*(n + 1)/2 - A048702[[n + 1]], {n, 0, 50}] (* G. C. Greubel, Sep 26 2017 *)

a01(n) = my(f); f = length(binary(n)) - 1; 2^(f+1)*n + sum(i=0, f, bittest(n, i) * 2^(f-i)); \\ A048701
a(n) = n*(n+1)/2 - a01(n)/3; \\ A006095

def A075113(n: int) -> int:
    s = bin(n)[2:]
    return n * (n + 1) // 2 - int(s + s[::-1], 2) // 3
print([A075113(n) for n in range(69)]) # Peter Luschny, Dec 14 2022

a(A000225(n)) = ((2^n)-1)*(2^(n-1)) - (2^(2n) - 1)/3 = A006095(n).

Definition corrected by Georg Fischer, Dec 13 2022

A171477 a(n) = 6a(n-1) - 8a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.

Original entry on oeis.org

1, 7, 35, 155, 651, 2667, 10795, 43435, 174251, 698027, 2794155, 11180715, 44731051, 178940587, 715795115, 2863245995, 11453115051, 45812722347, 183251413675, 733006703275, 2932028910251, 11728119835307, 46912487729835

Offset: 0

Klaus Brockhaus, Dec 09 2009

a(n) = A006095(n+2).
Second binomial transform of A168642.
Essentially partial sums of A006516.

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (7, -14, 8).

Cf. A006095 (Gaussian binomial coefficient [n, 2] for q=2), A168642 ((8*2^n+(-1)^n)/3, a(0)=1), A006516 (2^(n-1)*(2^n-1)), A171472, A171473.

[(8*4^n-6*2^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

{m=23; v=concat([1, 7], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+1); v}

a(n) = (8*4^n-6*2^n+1)/3.
G.f.: 1/((1-x)*(1-2*x)*(1-4*x)).
a(n) = A139250(2^(n+1) - 1). - Omar E. Pol, Dec 20 2012

A340312 Triangle read by rows: T(n,k) is the number of subsets of {0..2^n-1} with k elements such that the bitwise-xor of all the subset members gives zero, 0 <= k <= 2^n.

Original entry on oeis.org

1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 7, 14, 7, 0, 1, 1, 1, 1, 0, 35, 140, 273, 448, 715, 870, 715, 448, 273, 140, 35, 0, 1, 1, 1, 1, 0, 155, 1240, 6293, 27776, 105183, 330460, 876525, 2011776, 4032015, 7063784, 10855425, 14721280, 17678835, 18796230, 17678835, 14721280, 10855425, 7063784, 4032015, 2011776, 876525, 330460, 105183, 27776, 6293, 1240, 155, 0, 1, 1

Offset: 0

Jianing Song, Jan 04 2021

Sum_{k=0..2^n} T(n, k) gives the total number of subsets with bitwise-xor of all the subset members zero. There are in total 2^(2^n - n) such subsets of {0, 1, ..., 2^n-1}, see A300361 and the Mathematics Stack Exchange link below.
Equivalently, T(n, k) is the number of subsets of the vector space (F_2)^n such that the sum of elements in the subset is the zero vector.
T(n, k) is symmetric, that is, T(n, k) = T(n, 2^n-k) for k = 0..2^n, since if the bitwise-xor of the members in S is zero, then the complement of S in {0, 1, ..., 2^n-1} also has this property.

			Triangle begins:
[0]  1, 1;
[1]  1, 1, 0;
[2]  1, 1, 0, 1, 1;
[3]  1, 1, 0, 7, 14, 7, 0, 1, 1;
[4]  1, 1, 0, 35, 140, 273, 448, 715, 870, 715, 448, 273, 140, 35, 0, 1, 1;
[5]  1, 1, 0, 155, 1240, 6293, 27776, 105183, 330460, 876525, 2011776, 4032015, 7063784, 10855425, 14721280, 17678835, 18796230, 17678835, 14721280, 10855425, 7063784, 4032015, 2011776, 876525, 330460, 105183, 27776, 6293, 1240, 155, 0, 1, 1;
T(n,0) = 1 since the bitwise-xor of all the elements in the empty set is the identity of bitwise-xor (0), hence the empty set meets the requirement.
T(n,1) = 1 since the only such subset is {0}.
T(n,2) = 0 since no distinct a, b have a ^ b = 0.
T(n,3) = A006095(n): if distinct a, b, c have a ^ b ^ c = 0, then c = a ^ b, and a, b must both be nonzero since a = 0 implies b = c. On the other hand, if a, b are nonequal and are both nonzero, then c = a ^ b has c != a and c != b since c = a implies b = 0. So the total number of triples (a, b, c) is (2^n-1)*(2^n-2), and the total number of subsets {a, b, c} is (2^n-1)*(2^n-2)/3! = A006095(n).
T(n,4) = A016290(n-2): if distinct a, b, c, d have a ^ b ^ c ^ d = 0, then d = a ^ b ^ c. On the other hand, if a, b, c are distinct, then d = a ^ b ^ c has d != a, d != b, d != c since d = a implies b = c. So the total number of quadruples (a, b, c, d) is 2^n*(2^n-1)*(2^n-2), and the total number of subsets {a, b, c, d} is 2^n*(2^n-1)*(2^n-2)/4! = A016290(n-2).

Peter Luschny, Table of n, a(n) for n = 0..1032
Katrina Honigs and Graham McDonald, Theta characteristics and the fixed locus of [-1] on some varieties of Kummer type, arXiv:2307.13129 [math.AG], 2023. See pp. 6 and 22.
Mathematics Stack Exchange, Count subsets with zero sum of xors
Jianing Song, C Program for A340312, case n = 4

Cf. A000120 (hamming weight of n), A300361 (row sums).
Cf. A340263 (irreducible (?) factor if T(n,k) is seen as representing polynomials).
Cf. A340259(n) = T(n, 2^(n-1)), the central term of row n.
Cf. A340030 (case that only nonzero elements allowed).
Cf. A054669, A058878.
Cf. A006095 (k=3 column), A016290 (k=4 column); cf. also A010080-A010084 and A281123. - Jon E. Schoenfield, Jan 06 2021

/* Generating program for T(4,k), see link. */

A340312_row := proc(n) local a, b, c; c := 2^(n-1);
if n = 0 then return [1, 1] fi;
b := n -> add(binomial(2^n, 2*k)*x^(2*k), k = 0..2^n);
a := n -> x*mul(b(k), k = 0..n);
(x + 1)^c*(b(n-1) - (c-1)*a(n-2));
[seq(coeff(expand(%), x, j), j = 0..2*c)] end:
for n from 0 to 6 do A340312_row(n) od; # Peter Luschny, Jan 06 2021

T[n_, k_] := Binomial[2^n, k]/2^n + If[EvenQ[k], (-1)^(k/2)*(1-1/2^n)* Binomial[2^(n-1), k/2], 0];
Table[T[n, k], {n, 0, 5}, {k, 0, 2^n}] // Flatten (* Jean-François Alcover, Jan 14 2021, after Andrew Howroyd *)

T(n, k)={binomial(2^n, k)/2^n + if(k%2==0, (-1)^(k/2)*(1-1/2^n)*binomial(2^(n-1), k/2))} \\ Andrew Howroyd, Jan 09 2021

def A340312():
    a, b, c = 1, 1, 1
    yield [1, 1]
    yield [1, 1, 0]
    while True:
        c *= 2
        a *= b
        b = sum(binomial(c, 2 * k) * x^(2 * k) for k in range(c + 1))
        p = (x + 1)^c * (b - (c - 1) * x * a)
        yield expand(p).list()
A340312_row = A340312()
for _ in range(6):
    print(next(A340312_row)) # Peter Luschny, Jan 07 2021

T(n, k) = [x^k] p(n; x) where p(n; x) = (x + 1)^c*(b(n-1) - (c-1)*a(n-2)), b(n) = Sum_{k=0..2^n} binomial(2^n, 2*k)*x^(2*k), a(n) = x*Product_{k=0..n} b(k) and c = 2^(n-1), for n >= 1. - Peter Luschny, Jan 06 2021
T(n+1, k) = [x^k] (x+1)^(2^n)*p_n(x) where p_n(x) are the polynomials defined in A340263. - Peter Luschny, Jan 06 2021
From Andrew Howroyd, Jan 09 2021: (Start)
First take any subset of k-1 elements and append the bitwise-xor of the elements. The final element will either be a duplicate or not and consideration of the two cases leads to a formula linking T(n,k) and T(n,k-2) with binomial(2^n,k-1).
T(n, k) = (1/k)*(binomial(2^n,k-1) - (2^n-(k-2))*T(n,k-2)) for k >= 2.
T(n, k) = binomial(2^n, k)/2^n for odd k.
T(n, k) = binomial(2^n, k)/2^n + (-1)^(k/2)*(1-1/2^n)*binomial(2^(n-1), k/2) for even k.
T(n, k) = [x^k] ((1+x)^(2^n) + (2^n-1)*(1-x^2)^(2^(n-1)))/2^n.
T(n, k) = A340030(n,k-1) + A340030(n,k).
(End)

More terms from Andrew Howroyd and Jon E. Schoenfield.

A006120 Sum of Gaussian binomial coefficients [ n,k ] for q=6.

Original entry on oeis.org

1, 2, 9, 88, 2111, 118182, 16649389, 5547079988, 4671840869691, 9326302435784002, 47100039978152210249, 564020035264998031552848, 17088883834526416216141122391, 1227783027118593811726444427584862, 223195138386683651821176756496371359589

Offset: 0

N. J. A. Sloane

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Vincenzo Librandi, Table of n, a(n) for n = 0..70
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)

[n le 2 select n else 2*Self(n-1)+(6^(n-2)-1)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 13 2016

Flatten[{1,RecurrenceTable[{a[n]==2*a[n-1]+(6^(n-1)-1)*a[n-2],a[0]==1,a[1]==2},a,{n,1,15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)
Table[Sum[QBinomial[n, k, 6], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2016 *)

a(n) = 2*a(n-1)+(6^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013

a(n) ~ c * 6^(n^2/4), where c = EllipticTheta[3,0,1/6]/QPochhammer[1/6,1/6] = 1.656816524577... if n is even and c = EllipticTheta[2,0,1/6]/QPochhammer[1/6,1/6] = 1.630173070572... if n is odd. - Vaclav Kotesovec, Aug 21 2013

A022190 Gaussian binomial coefficients [n, 7] for q = 2.

Original entry on oeis.org

1, 255, 43435, 6347715, 866251507, 114429029715, 14877590196755, 1919209135381395, 246614610741341843, 31627961868755063955, 4052305562169692070035, 518946525150879134496915, 66441249531569955747981459

Offset: 7

N. J. A. Sloane, Jun 14 1998

Vincenzo Librandi, Table of n, a(n) for n = 7..200

Gaussian binomial coefficient [n, k] for q = 2: A000225 (k = 1), A006095 (k = 2), A006096 (k = 3), A006097 (k = 4), A006110 (k = 5), A022189 - A022195 (k = 6 thru 12).

r:=7; q:=2; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016

Table[QBinomial[n, 7, 2], {n, 7, 24}] (* Vincenzo Librandi, Aug 02 2016 *)

r=7; q=2; for(n=r,30, print1(prod(j=1,r,(1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, May 30 2018

[gaussian_binomial(n,7,2) for n in range(7,20)] # Zerinvary Lajos, May 25 2009

G.f.: x^7/((1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)*(1-64*x)*(1-128*x)). - Vincenzo Librandi, Aug 07 2016
a(n) = Product_{i=1..7} (2^(n-i+1)-1)/(2^i-1), by definition. - Vincenzo Librandi, Aug 02 2016
G.f. with an offset of 0: exp( Sum_{n >= 1} b(8*n)/b(n)*x^n/n ) = 1 + 255*x + 43435*x^2 + ..., where b(n) = A000225(n) = 2^n - 1. - Peter Bala, Jul 01 2025

Changed offset by Vincenzo Librandi, Aug 02 2016

A060484 Number of 6-block tricoverings of an n-set.

Original entry on oeis.org

1, 95, 3107, 75835, 1653771, 34384875, 700030507, 14116715435, 283432939691, 5679127043755, 113683003777707, 2274630646577835, 45502044971338411, 910133025632152235, 18203564201836161707, 364080180268471397035

Offset: 3

Vladeta Jovovic, Mar 20 2001

A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.

Andrew Howroyd, Table of n, a(n) for n = 3..200
Index entries for linear recurrences with constant coefficients, signature (45,-720,5220,-17664,25920,-12800).

Column k=6 of A060487.

Cf. A006095, A060483, A060485, A060486, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.

With[{c=1/6!},Table[c(20^n-6*10^n-15*8^n+135*4^n-310*2^n+240),{n,3,20}]] (* or *) LinearRecurrence[{45,-720,5220,-17664,25920,-12800},{1,95,3107,75835,1653771,34384875},20] (* Harvey P. Dale, Jan 05 2017 *)

a(n) = (1/6!)*(20^n - 6*10^n - 15*8^n + 135*4^n - 310*2^n + 240) \\ Andrew Howroyd, Dec 15 2018

a(n) = (1/6!)*(20^n - 6*10^n - 15*8^n + 135*4^n - 310*2^n + 240).
E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..inf}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).
G.f.: -x^3*(800*x^3+448*x^2-50*x-1) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(10*x-1)*(20*x-1)). - Colin Barker, Jan 12 2013
a(n) = 45*a(n-1)-720*a(n-2)+5220*a(n-3)-17664*a(n-4)+25920*a(n-5)-12800*a(n-6). - Wesley Ivan Hurt, Oct 18 2021

A060485 Number of 7-block tricoverings of an n-set.

Original entry on oeis.org

43, 4520, 244035, 10418070, 401861943, 14778678180, 530817413155, 18837147108890, 664260814445943, 23345018969140440, 818942064306004275, 28699514624047140510, 1005201938765467579543, 35196266296400319440300

Offset: 4

Vladeta Jovovic, Mar 20 2001

A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.

Andrew Howroyd, Table of n, a(n) for n = 4..200
Index entries for linear recurrences with constant coefficients, signature (110, -4991, 124120, -1887459, 18470550, -118758569, 501056740, -1355000500, 2223560000, -1973160000, 705600000).

Column k=7 of A060487.

Cf. A006095, A060483, A060484, A060486, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.

a(n) = (1/7!)*(35^n - 7*20^n - 21*15^n + 42*10^n + 105*8^n + 105*7^n + 70*5^n - 945*4^n - 525*3^n + 2450*2^n - 1470).
E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..infinity}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).
G.f.: x^4*(27300000*x^7 +9288000*x^6 -17908650*x^5 +6008735*x^4 -796380*x^3 +38552*x^2 +210*x -43) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(7*x -1)*(8*x -1)*(10*x -1)*(15*x -1)*(20*x -1)*(35*x -1)). - Colin Barker, Jan 12 2013

A249993 Expansion of 1/((1+x)(1+2x)(1-4x)).

Original entry on oeis.org

1, 1, 11, 29, 147, 525, 2227, 8653, 35123, 139469, 559923, 2235597, 8950579, 35785933, 143176499, 572640461, 2290692915, 9162509517, 36650562355, 146601200845, 586406900531, 2345623407821, 9382502019891, 37529991302349, 150119998763827, 600479927946445

Offset: 0

Alex Ratushnyak, Dec 27 2014

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,10,8).

Cf. A249992.
Cf. A006095, A171477 for g.f. 1/((1-x)*(1-2*x)*(1-4*x)).
Cf. A015249, A084152, A084175 for g.f. 1/((1-x)*(1+2*x)*(1-4*x)).
Cf. A109765 for g.f. 1/((1+x)*(1-2*x)*(1-4*x)).

[(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15: n in [0..40]]; // G. C. Greubel, Oct 10 2022

CoefficientList[Series[1/((1+x)(1+2x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{1,10,8},{1,1,11},30] (* Harvey P. Dale, Dec 13 2018 *)

Vec(1/((1+x)*(1+2*x)*(1-4*x)) + O(x^40)) \\ Michel Marcus, Dec 28 2014

[(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15 for n in range(41)] # G. C. Greubel, Oct 10 2022

G.f.: 1/((1+x)*(1+2*x)*(1-4*x)).
a(n) = ( 2^(3+2*n) + (5*2^(1+n) - 3)*(-1)^n )/15. Colin Barker, Dec 28 2014
a(n) = a(n-1) + 10*a(n-2) + 8*a(n-3). - Colin Barker, Dec 28 2014
E.g.f.: (1/15)*(10*exp(-2*x) - 3*exp(-x) + 8*exp(4*x)). - G. C. Greubel, Oct 10 2022

A359985 Triangle read by rows: T(n,k) is the number of quasi series-parallel matroids on [n] with rank k, 0 <= k <= n.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 35, 15, 1, 1, 31, 155, 155, 31, 1, 1, 63, 651, 1365, 651, 63, 1, 1, 127, 2667, 10941, 10941, 2667, 127, 1, 1, 255, 10795, 82215, 156597, 82215, 10795, 255, 1, 1, 511, 43435, 589135, 1988007, 1988007, 589135, 43435, 511, 1

Offset: 0

Andrew Howroyd, Mar 08 2023

A quasi series-parallel matroid is a collection of series-parallel matroids. See the Ferroni/Larson reference for a precise definition.

The first six rows of this triangle are the same as A022166.

			Triangle begins:
  1;
  1,   1;
  1,   3,    1;
  1,   7,    7,     1;
  1,  15,   35,    15,     1;
  1,  31,  155,   155,    31,    1;
  1,  63,  651,  1365,   651,   63,   1;
  1, 127, 2667, 10941, 10941, 2667, 127, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
Luis Ferroni and Matt Larson, Kazhdan-Lusztig polynomials of braid matroids, arXiv:2303.02253 [math.CO], 2023.
Nicholas Proudfoot, Yuan Xu, and Ben Young, On the enumeration of series-parallel matroids, arXiv:2406.04502 [math.CO], 2024.

Row sums are A359986.
Columns k=0..2 are A000012, A000225, A006095.
Cf. A022166, A140945.

\\ Proposition 2.3, 2.8 in Ferroni/Larson, compare A140945.
T(n) = {[Vecrev(p) | p<-Vec(serlaplace(exp(x*(y+1) + y*intformal( serreverse(log(1 + x*y + O(x^n))/y + log(1 + x + O(x^n)) - x)))))]}
{ my(A=T(8)); for(i=1, #A, print(A[i])) }

A006098 Gaussian binomial coefficient [ 2n,n ] for q=2.

Original entry on oeis.org

1, 3, 35, 1395, 200787, 109221651, 230674393235, 1919209135381395, 63379954960524853651, 8339787869494479328087443, 4380990637147598617372537398675, 9196575543360038413217351554014467475, 77184136346814161837268404381760884963259795

Offset: 0

N. J. A. Sloane

nonn

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

T. D. Noe, Table of n, a(n) for n = 0..35
Alin Bostan and Sergey Yurkevich, On the q-analogue of Pólya's Theorem, arXiv:2109.02406 [math.CO], 2021.
I. Siap and I. Aydogdu, Counting The Generator Matrices of Z_2 Z_8 Codes, arXiv:1303.6985 [math.CO], 2013.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)
Eric Weisstein's World of Mathematics, q-Binomial Coefficient.

Cf. A022166, A065446.

q:=2; [n le 0 select 1 else (&*[(1-q^(2*n-j))/(1-q^(j+1)): j in [0..n-1]]): n in [0..15]]; // G. C. Greubel, Mar 09 2019

Table[QBinomial[2n,n,2],{n,0,20}] (* Harvey P. Dale, Oct 22 2012 *)

q=2; {a(n) = prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1))) };
vector(10, n, n--; a(n)) \\ G. C. Greubel, Mar 09 2019

[gaussian_binomial(2*n,n,2) for n in range(0,11)] # Zerinvary Lajos, May 25 2009

a(n) = A022166(2n,n). - Alois P. Heinz, Mar 30 2016
a(n) ~ c * 2^(n^2), where c = A065446. - Vaclav Kotesovec, Sep 22 2016
a(n) = Sum_{k=0..n} 2^(k^2)*(A022166(n,k))^2. - Werner Schulte, Mar 09 2019

More terms from Harvey P. Dale, Oct 22 2012

cp's OEIS Frontend

A075113 a(n) = A000217(n) - A048702(n).

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A171477 a(n) = 6*a(n-1) - 8*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.

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A340312 Triangle read by rows: T(n,k) is the number of subsets of {0..2^n-1} with k elements such that the bitwise-xor of all the subset members gives zero, 0 <= k <= 2^n.

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A006120 Sum of Gaussian binomial coefficients [ n,k ] for q=6.

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A022190 Gaussian binomial coefficients [n, 7] for q = 2.

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A060484 Number of 6-block tricoverings of an n-set.

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A060485 Number of 7-block tricoverings of an n-set.

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A171477 a(n) = 6a(n-1) - 8a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.

A249993 Expansion of 1/((1+x)(1+2x)(1-4x)).