A026644 -id:A026644 - cp's OEIS frontend

A026643 a(n) = A026637(n, floor(n/2)).

1, 1, 2, 4, 8, 13, 26, 46, 92, 166, 332, 610, 1220, 2269, 4538, 8518, 17036, 32206, 64412, 122464, 244928, 467842, 935684, 1794196, 3588392, 6903352, 13806704, 26635774, 53271548, 103020253, 206040506, 399300166, 798600332

Offset: 0

Clark Kimberling

nonn

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

Cf. A026637, A026638, A026639, A026640, A026641, A026642, A026644.

Cf. A026966, A026967, A026968, A026969, A026970.

[1] cat [n le 4 select 2^(n-1) else (4*Self(n-1) +(7*n-9)*Self(n-2) +2*Self(n-3) +4*(n-1)*Self(n-4))/(2*(n+1)): n in [1..40]]; // G. C. Greubel, Jul 01 2024

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[(3*n -1)/2], T[n-1,k-1] + T[n-1,k] ]]; (* A026637 *)
A026643[n_]:= T[n, Floor[n/2]];
Table[A026643[n], {n,0,40}] (* G. C. Greubel, Jul 01 2024 *)

@CachedFunction
def a(n): # a = A026643
    if n<5: return (1,1,2,4,8)[n]
    else: return (4*a(n-1) +(7*n-9)*a(n-2) +2*a(n-3) +4*(n-1)*a(n-4))/(2*(n+1))
[a(n) for n in range(41)] # G. C. Greubel, Jul 01 2024

a(n) = (4*a(n-1) + (7*n-9)*a(n-2) + 2*a(n-3) + 4*(n-1)*a(n-4))/(2*(n+1)) with a(0) = a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8. - G. C. Greubel, Jul 01 2024

A026646 a(n) = Sum_{i=0..n} Sum_{j=0..n} A026637(i,j).

Original entry on oeis.org

1, 3, 7, 17, 37, 79, 163, 333, 673, 1355, 2719, 5449, 10909, 21831, 43675, 87365, 174745, 349507, 699031, 1398081, 2796181, 5592383, 11184787, 22369597, 44739217, 89478459, 178956943, 357913913, 715827853, 1431655735

Offset: 0

Clark Kimberling

nonn

a(n) indexes the corner blocks on the Jacobsthal spiral built from blocks of unit area (using J(1) and J(2) as the sides of the first block). - Paul Barry, Mar 06 2008

Partial sums of A026644, which are the row sums of A026637. - Paul Barry, Mar 06 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Cf. A000126, A001045, A026637, A026644, A084639, A109613.
Cf. A026637, A026638, A026639, A026640, A026641, A026642, A026643.
Cf. A026644, A026966, A026967, A026968, A026969, A026970.

[(2^(n+4) -(6*n+9+(-1)^n))/6: n in [0..40]]; // G. C. Greubel, Jul 01 2024

CoefficientList[Series[(1-x^2+2x^3)/((1-x)(1-2x)(1-x^2)), {x, 0, 29}], x] (* Metin Sariyar, Sep 22 2019 *)
LinearRecurrence[{3,-1,-3,2}, {1,3,7,17}, 41] (* G. C. Greubel, Jul 01 2024 *)

[(2^(n+4) - (-1)^n -9 - 6*n)/6 for n in range(41)] # G. C. Greubel, Jul 01 2024

G.f.: (1 -x^2 +2*x^3)/((1-x)*(1-2*x)*(1-x^2)). - Ralf Stephan, Apr 30 2004
From Paul Barry, Mar 06 2008: (Start)
a(n) = A001045(n+3) - 2*floor((n+2)/2).
a(n) = -n + Sum_{k=0..n} A001045(k+2) = A084639(n+1) - n. (End)
a(n+1) = 2*a(n) + A109613(n), a(0)=1. - Paul Curtz, Sep 22 2019

A026647 a(n) = Sum_{k=0..floor(n/2)} A026637(n-k, k).

Original entry on oeis.org

1, 1, 2, 3, 6, 10, 17, 27, 45, 73, 119, 192, 312, 505, 818, 1323, 2142, 3466, 5609, 9075, 14685, 23761, 38447, 62208, 100656, 162865, 263522, 426387, 689910, 1116298, 1806209, 2922507, 4728717, 7651225, 12379943, 20031168

Offset: 0

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,-1,-1).

Cf. A026637, A026638, A026639, A026640, A026641, A026642, A026643.
Cf. A026644, A026645, A026646, A026966, A026967, A026968, A026969.
Cf. A026970.

[1] cat [n le 5 select Binomial(n, Floor(n/2)) else Self(n-2) +Self(n-3) +2*Self(n-4) +Self(n-5) +3: n in [1..40]]; // G. C. Greubel, Jul 01 2024

a[n_]:= a[n]= If[n<6, Binomial[n, Floor[n/2]], a[n-2] +a[n-3] +2*a[n- 4] +a[n-5] +3]; (* a = A026647 *)
Table[a[n], {n,0,40}] (* G. C. Greubel, Jul 01 2024 *)
LinearRecurrence[{1,1,0,1,-1,-1},{1,1,2,3,6,10,17},40] (* Harvey P. Dale, Jan 19 2025 *)

@CachedFunction
def a(n): # a = A026647
    if n<6: return binomial(n, n//2)
    else: return a(n-2) + a(n-3) + 2*a(n-4) + a(n-5) + 3
[a(n) for n in range(41)] # G. C. Greubel, Jul 01 2024

G.f.: (1 + x^5 + x^6)/((1-x^4)*(1-x-x^2)).
From G. C. Greubel, Jul 01 2024: (Start)
a(n) = [n=0] - (3/4) + (1/4)*(-1)^n - (1/10)*2^((1-(-1)^n)/2)*(-1)^floor((n+1)/2) + (3/5)*LucasL(n+1).
a(n) = (1/20)*( 12*LucasL(n+1) + 5*(-1)^n - 15 - 2*cos(n*Pi/2) + 4*sin(n*Pi/2) ) + [n=0].
a(n) = a(n-2) + a(n-3) + 2*a(n-4) + a(n-5) + 3, with a(0) = a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 6, a(5) = 10. (End)

A026645 a(n) = Sum_{k=0..floor(n/2)} A026637(n, k).

Original entry on oeis.org

1, 1, 3, 5, 14, 21, 55, 85, 216, 341, 848, 1365, 3340, 5461, 13191, 21845, 52208, 87381, 206968, 349525, 821514, 1398101, 3264044, 5592405, 12979006, 22369621, 51642594, 89478485, 205592744, 357913941, 818848135, 1431655765, 3262611696, 5726623061, 13003800704, 22906492245

Offset: 0

Clark Kimberling

nonn

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

Cf. A026637, A026638, A026639, A026640, A026642, A026643, A026644.

Cf. A026646, A026647, A026966, A026967, A026968, A026969, A026970.

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[(3*n- 1)/2], T[n-1,k] + T[n-1,k-1] ]];
A026645[n_]:= Sum[T[n, k], {k, 0, Floor[n/2]}];
Table[A026645[n], {n,0,40}] (* G. C. Greubel, Jun 29 2024 *)

@CachedFunction
def T(n,k): # T = A026637
    if k==0 or k==n: return 1
    elif k==1 or k==n-1: return ((3*n-1)//2)
    else: return T(n-1, k) + T(n-1, k-1)
def A026645(n): return sum(T(n,k) for k in range((n//2)+1))
[A026645(n) for n in range(41)] # G. C. Greubel, Jun 29 2024

A052953 Expansion of 2(1-x-x^2)/((1-x)(1+x)(1-2x)).

Original entry on oeis.org

2, 2, 4, 6, 12, 22, 44, 86, 172, 342, 684, 1366, 2732, 5462, 10924, 21846, 43692, 87382, 174764, 349526, 699052, 1398102, 2796204, 5592406, 11184812, 22369622, 44739244, 89478486, 178956972, 357913942, 715827884, 1431655766, 2863311532

Offset: 0

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

a(n) = sum of absolute values of terms in the (n+1)-th row of the triangle in A108561; - Reinhard Zumkeller, Jun 10 2005
a(n) = A078008(n+1) + 2*(1 + n mod 2). - Reinhard Zumkeller, Jun 10 2005
Essentially the same as A128209. - R. J. Mathar, Jun 14 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1024
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Apart from initial term, equals A026644(n+1) + 2.

Cf. A001045.

List([0..40], n-> (2^(n+1) +3 +(-1)^n)/3); # G. C. Greubel, Oct 21 2019

[(2^(n+1) +3 +(-1)^n)/3: n in [0..40]]; // G. C. Greubel, Oct 21 2019

spec:= [S,{S=Union(Sequence(Union(Prod(Union(Z,Z),Z),Z)),Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
seq((2^(n+1) +3 +(-1)^n)/3, n=0..40); # G. C. Greubel, Oct 21 2019

LinearRecurrence[{2,1,-2}, {2,2,4}, 40] (* G. C. Greubel, Oct 22 2019 *)
CoefficientList[Series[2(1-x-x^2)/((1-x)(1+x)(1-2x)),{x,0,40}],x] (* Harvey P. Dale, Aug 03 2025 *)

vector(41, n, (2^n +3 -(-1)^n)/3 ) \\ G. C. Greubel, Oct 21 2019

[(2^(n+1) +3 +(-1)^n)/3 for n in (0..40)] # G. C. Greubel, Oct 21 2019

G.f.: 2*(1-x-x^2)/((1-x^2)*(1-2*x)).
a(n) = a(n-1) + 2*a(n-2) - 2.
a(n) = 1 + Sum_{alpha=RootOf(-1+z+2*z^2)} (1 + 4*alpha)*alpha^(-1-n)/9.
a(2n) = 2*a(n-1)-2, a(2n+1) = 2*a(2n). - Lee Hae-hwang, Oct 11 2002
From Paul Barry, May 24 2004: (Start)
a(n) = A001045(n+1) + 1.
a(n) = (2^(n+1) - (-1)^(n+1))/3 + 1. (End)
E.g.f.: (2*exp(2*x) + 3*exp(x) + exp(-x))/3. - G. C. Greubel, Oct 21 2019

More terms from James Sellers, Jun 05 2000

A167030 a(n) = (2^n - (-1)^n - 3)/3.

Original entry on oeis.org

-1, 0, 0, 2, 4, 10, 20, 42, 84, 170, 340, 682, 1364, 2730, 5460, 10922, 21844, 43690, 87380, 174762, 349524, 699050, 1398100, 2796202, 5592404, 11184810, 22369620, 44739242, 89478484, 178956970, 357913940, 715827882

Offset: 0

Paul Curtz, Oct 27 2009

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..240 from Vincenzo Librandi)
Nicolas Gastineau and O. Togni, On S-packing edge-colorings of cubic graphs, arXiv preprint arXiv:1711.10906 [cs.DM], 2017.
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

A026644 is an essentially identical sequence.

Cf. A001045, A153772, A047849, A020988, A000975.

[(2^n-(-1)^n)/3 -1: n in [0..40] ]; // Vincenzo Librandi, Apr 28 2011

f[n_] := (2^n - (-1)^n - 3)/3; Array[f, 32, 0]

a(n)=(2^n-(-1)^n)/3-1 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = A001045(n) - 1.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
G.f.: (1 - 2*x - x^2)/((x^2 - 1)*(1-2*x)).
2*a(n) = A153772(n+1).
a(2n+1) - a(2n) = A047849(n).
a(2n+1) = A020988(n); a(2n+2) = 2*A020988(n).
a(n+2) = 2*A000975(n).
a(2n+2) = a(2n) + 2^(2n).
E.g.f.: (1/3)*(exp(2*x) - 3*exp(x) - exp(-x)). - G. C. Greubel, May 30 2016

Edited by R. J. Mathar, Dec 17 2010

A084170 a(n) = (5*2^n + (-1)^n - 3)/3.

Original entry on oeis.org

1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, 3412, 6826, 13652, 27306, 54612, 109226, 218452, 436906, 873812, 1747626, 3495252, 6990506, 13981012, 27962026, 55924052, 111848106, 223696212, 447392426, 894784852, 1789569706, 3579139412

Offset: 0

Paul Barry, May 18 2003

Original name of this sequence: Generalized Jacobsthal numbers.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Cf. A000975, A002450, A026644, A146882, A169969.

Cf. A000225 (Mersenne numbers), A001045 (Jacobsthal numbers).

[(5*2^n +(-1)^n)/3 -1: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011

LinearRecurrence[{2,1,-2},{1,2,6},40] (* or *) Table[(5*2^n+(-1)^n-3)/3,{n,0,40}] (* Harvey P. Dale, Jan 29 2012 *)

a(n)=(5*2^n)\/3-1 \\ Charles R Greathouse IV, Jul 01 2011

[(2/3)*(5*2^(n-1) -1 -(n%2)) for n in range(41)] # G. C. Greubel, Oct 11 2022

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n>2.
a(n) = a(n-1) + 2*a(n-2) + 2, a(0)=1, a(1)=2.
G.f.: (1+x^2)/((1+x)*(1-x)*(1-2*x)).
E.g.f.: 5*exp(2*x)/3 - exp(x) + exp(-x)/3.
a(n+1) = A000975(n+2) + A000975(n).
a(2*n+1) - 2 = 10*A000975(n).
a(2*n+2) - 6 = 20*A000975(n).
a(n+2*k) - a(n) = 5*A002450(k)*2^n = A146882(k-1)*2^n, k >= 0. - Paul Curtz, Jun 15 2011
From Yosu Yurramendi, Jul 05 2016: (Start)
a(n) = A169969(2n) - 1, n >= 1; a(n) = 3*2^(n-1) - 1 + A169969(2n-7), n >= 5.
a(n+3) = 15*2^n - 2 - a(n), n >= 0, a(0)=1, a(1)=2, a(2)=6.
a(n) + A026644(n) = 3*2^n - 2, n >= 1.
a(n+3) = 3*2^(n+2) + A026644(n), n >= 1. (End)
a(n) = A000225(n+1) - A001045(n). - Yuchun Ji, Mar 17 2020

A103196 a(n) = (1/9)(2^(n+3)-(-1)^n(3n-1)).

Original entry on oeis.org

1, 2, 3, 8, 13, 30, 55, 116, 225, 458, 907, 1824, 3637, 7286, 14559, 29132, 58249, 116514, 233011, 466040, 932061, 1864142, 3728263, 7456548, 14913073, 29826170, 59652315, 119304656, 238609285, 477218598, 954437167

Offset: 0

Creighton Dement, Mar 18 2005

A floretion-generated sequence relating to the Jacobsthal sequence A001045 as well as to A095342 (Number of elements in n-th string generated by a Kolakoski(5,1) rule starting with a(1)=1). (a(n)) may be seen as the result of a certain transform of the natural numbers (see program code).

Floretion Algebra Multiplication Program, FAMP Code: 4jesleftforseq[A*B] with A = + 'i + 'j + i' + j' + 'ii' + 'jj' + 'ij' + 'ji' + e and B = - .25'i + .25'j + .25'k + .25i' - .25j' + .25k' - .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' - .25'ki' - .25'kj' - .25e; 1vesforseq[A*B](n) = n, ForType: 1A.

Index entries for linear recurrences with constant coefficients, signature (0,3,2).

Cf. A001045, A095342, A053088, A034299, A052953, A026644.

Table[(2^(n+3)-(-1)^n (3n-1))/9,{n,0,30}] (* or *) LinearRecurrence[ {0,3,2},{1,2,3},40] (* Harvey P. Dale, Jul 09 2018 *)

G.f. (2x+1)/((1-2x)(x+1)^2); Superseeker results: a(n) + a(n+1) = A001045(n+3); a(n+1) - a(n) = A095342(n+1); a(n+2) - a(n+1) - a(n) = A053088(n+1) = A034299(n+1) - A034299(n); a(n) + 2a(n+1) + a(n+2) = 2^(n+3); a(n+2) - 2a(n+1) + a(n) = A053088(n+1) - A053088(n); a(n+2) - a(n) = A001045(n+4) - A001045(n+3) = A052953(n+3) - A052953(n+2) = A026644(n+2) - A026644(n+1);

a(n)=sum{k=0..n+2, (-1)^(n-k)*C(n+2, k)phi(phi(3^k))}; a(n)=sum{k=0..n+2, (-1)^(n-k)*C(n+2, k)(2*3^k/9+C(1, k)/3+4*C(0, k)/9)}; a(n)=sum{k=0..n+2, J(n-k+3)((-1)^(k+1)-2C(1, k)+4C(0, k))} where J(n)=A001045(n); a(n)=A113954(n+2). - Paul Barry, Nov 09 2005

A169969 Locations of row maxima in "crushed" version of Stern's diatomic array.

Original entry on oeis.org

1, 3, 5, 7, 11, 13, 21, 27, 43, 53, 85, 107, 171, 213, 341, 427, 683, 853, 1365, 1707, 2731, 3413, 5461, 6827, 10923, 13653, 21845, 27307, 43691, 54613, 87381, 109227, 174763, 218453, 349525, 436907, 699051, 873813, 1398101, 1747627, 2796203, 3495253, 5592405

Offset: 1

N. J. A. Sloane, Aug 08 2010

From Michel Marcus, Jan 22 2015: (Start)
The Stern's diatomic array begins (see A049456).
  1...............................1
  1...............2...............1
  1.......3.......2.......3.......1
  1...4...3...5...2...5...3...4...1
  1.5.4.7.3.8.5.7.2.7.5.8.3.7.4.5.1
  ...
The "crushed" version is obtained by removing the right column, and then squeezing everything to the left.
  1;
  1, 2;
  1, 3, 2, 3;
  1, 4, 3, 5, 2, 5, 3, 4;
  1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5;
  ...
This gives sequence 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, ... (cf. A002487).
The "crushed" array row maxima are: 1, 2, 3, 5, 8, ... (cf. A000045).
The indices of these values in A002487 are 1, 3, 5, 7, 11, ... : this sequence.
Note, for instance, that for 3rd row, the maximum which is 3, appears twice, at indices 5 and 7, giving 2 terms for this sequence.
(End)

			G.f. = x + 3*x^2 + 5*x^3 + 7*x^4 + 11*x^5 + 13*x^6 + 21*x^7 + 27*x^8 + 43*x^9 + ...

S. Northshield, Stern's diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, ..., Amer. Math. Monthly, 117 (2010), 581-598.
Index entries for linear recurrences with constant coefficients, signature (0,1,0,2).

Cf. A000079, A026644, A048573, A049456, A084170, A168642.

a[n_] := a[n] = If[n <= 5, {1, 3, 5, 7, 11}[[n]], a[n-2] + 2a[n-4]]; Array[a, 42] (* Jean-François Alcover, Dec 11 2016 *)

fusc(n)=local(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); b; \\ from A002487
lista(nn) = {nb = 2^(nn+1)-1; vall = vector(nb, n, fusc(n)); for (n=1, nn, vmax = 0; for (j=2^(n-1), 2^n-1, if (vall[j] > vmax, vmax = vall[j]);); for (j=2^(n-1), 2^n-1, if (vall[j] == vmax, print1(j, ", "));););} \\ Michel Marcus, Jan 22 2015

a(2n+1) + a(2n+2) = 3*2^(n+1), n>0 . - Yosu Yurramendi, Jun 29 2016
a(2n+3) = 3*2^(n+1) - a(n); a(2n+4) = 3*2^(n+1) + a(n), n>=0, a(0)=0 (new term), a(1)=1, a(2)=3 . - Yosu Yurramendi, Jun 29 2016
G.f.: x*(1 + 3*x + 4*x^2 + 4*x^3 + 4*x^4)/((1 + x^2)*(1 - 2*x^2)). - Ilya Gutkovskiy, Jun 29 2016
For n>1, a(n) = (2^(n/2 - 1)*(5 + 4*sqrt(2) + (-1)^n*(5 - 4*sqrt(2))) + cos(Pi*n/2) + sin(Pi*n/2))/3. - Vaclav Kotesovec, Jun 30 2016
a(2n) = a(2n-7) + 3*2^(n-1); a(2n-1) = a(2n-7) - 3*2^(n-1), n>=5 . - Yosu Yurramendi, Jul 06 2016
a(2n-1) = A168642(n), n>0; a(2n) = A048573(n), n>0; a(2n-1) = A026644(n) + 1, n>1; a(2n) = A084170(n) + 1, n>0 . - Yosu Yurramendi, Dec 11 2016

More terms from Michel Marcus, Jan 22 2015

A174395 The number of different 4-colorings for the vertices of all triangulated planar polygons on a base with n vertices if the colors of two adjacent boundary vertices are fixed.

Original entry on oeis.org

0, 2, 10, 40, 140, 462, 1470, 4580, 14080, 42922, 130130, 393120, 1184820, 3565382, 10717990, 32197660, 96680360, 290215842, 870997050, 2613690200, 7842468700, 23530202302, 70596199310, 211799782740, 635421717840, 1906309892762, 5719019156770, 17157236427280

Offset: 3

Patrick Labarque, Mar 18 2010, Mar 21 2010

1st: The number of different vertex colorings with 4 or 3 colors for n vertices is: (3^(n-1)-2-(-1)^n)/4.
2nd: The number of 3-colorings is: (2^n -3-(-1)^n)/3.
The above sequence is the difference between the first and the second one.

			n=3 then a(3)=0 as there are no 4-colorings for the only triangle.
n=4 then a(4)=2 as there are six good colorings less four 3-colorings for the two triangulated quadrilaterals (4-gons).
n=5 then a(5)=10 as there are twenty good colorings less ten 3-colorings for the five triangulated pentagons.

Vincenzo Librandi, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (5,-5,-5,6).

Equals A081251 (2,6,20...) minus A026644 (2,4,10...)

[(3^n - 2^(n+2) + 6 + (-1)^n) / 12: n in [3..30]]; // Vincenzo Librandi, Sep 23 2013

CoefficientList[Series[-2 x/((x - 1) (x + 1) (2 x - 1) (3 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 23 2013 *)
LinearRecurrence[{5,-5,-5,6},{0,2,10,40},30] (* Harvey P. Dale, Aug 29 2015 *)

Vec(-2*x^4/((x-1)*(x+1)*(2*x-1)*(3*x-1))  + O(x^100)) \\ Colin Barker, Sep 22 2013

a(n) = (3^n - 2^(n+2) + 6 + (-1)^n) / 12.

a(n) = 5*a(n-1)-5*a(n-2)-5*a(n-3)+6*a(n-4). G.f.: -2*x^4 / ((x-1)*(x+1)*(2*x-1)*(3*x-1)). - Colin Barker, Sep 22 2013

More terms from Colin Barker, Sep 22 2013

cp's OEIS Frontend

A026643 a(n) = A026637(n, floor(n/2)).

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A026646 a(n) = Sum_{i=0..n} Sum_{j=0..n} A026637(i,j).

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A026647 a(n) = Sum_{k=0..floor(n/2)} A026637(n-k, k).

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A026645 a(n) = Sum_{k=0..floor(n/2)} A026637(n, k).

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A052953 Expansion of 2*(1-x-x^2)/((1-x)*(1+x)*(1-2*x)).

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A167030 a(n) = (2^n - (-1)^n - 3)/3.

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A084170 a(n) = (5*2^n + (-1)^n - 3)/3.

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A052953 Expansion of 2(1-x-x^2)/((1-x)(1+x)(1-2x)).