A003947 -id:A003947 - cp's OEIS frontend

A292540 Number of 3-cycles in the n-Sierpinski tetrahedron graph.

4, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080, 351843720888320, 1407374883553280

Offset: 1

Eric W. Weisstein, Sep 18 2017

nonn

Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Sierpinski Tetrahedron Graph
Index entries for linear recurrences with constant coefficients, signature (4).

Cf. A003947, A269696.

Cf. A292542 (4-cycles), A292543 (5-cycles), A292545 (6-cycles).

Table[If[n == 1, 4, 5 4^(n - 1)], {n, 10}]
Join[{4}, LinearRecurrence[{4}, {20}, 30]]
CoefficientList[Series[-((4 (1 + x))/(-1 + 4 x)), {x, 0, 20}], x]
Join[{4},NestList[4#&,20,30]] (* Harvey P. Dale, Sep 21 2019 *)

a(n) = 5*4^(n - 1) for n > 1.
a(n) = 4*a(n-1) for n > 2.
G.f. -4*x*(1 + x)/(-1 + 4 x).

A347839 An array of the positive integers congruent to 2 modulo 3 (A016789), read by antidiagonals upwards, giving the present triangle.

Original entry on oeis.org

2, 5, 8, 11, 20, 32, 14, 44, 80, 128, 17, 56, 176, 320, 512, 23, 68, 224, 704, 1280, 2048, 26, 92, 272, 896, 2816, 5120, 8192, 29, 104, 368, 1088, 3584, 11264, 20480, 32768, 35, 116, 416, 1472, 4352, 14336, 45056, 81920, 131072, 38, 140, 464, 1664, 5888, 17408, 57344, 180224, 327680, 524288

Offset: 1

Wolfdieter Lang, Oct 21 2021

This array a = (a(k, n))_{k >= 1,n >= 0} is underlying array A of A347834. See the first formula. It has a simple recurrence for the rows k, given the first column a(k, 0) = A347838(k), which lists the positive integers congruent to {2, 5, 11} modulo 12.
In the array one can add the negative of the powers of 4 as row for k = 0, i.e., -A000302(n), for n >= 0.
All positive numbers congruent to 2 modulo 3 (A017617) appear once in this array. Proof from the array A of A347834 of the positive integers congruent to {1,3,5,7} modulo 8, and the present first formula: The members of column n = 0 give all the positive integers congruent to {2, 5, 11} modulo 12 once, and the members of columns n >= 1 give all the positive integers congruent to 8 modulo 12 (A017617) once. These members combined lead to the positive integers congruent to 2 modulo 3.

			The array a(k, n) begins:
k \ n  0   1   2    3    4     5      6      7       8       9       10 ...
---------------------------------------------------------------------------
1:     2   8  32  128  512  2048   8192  32768  131072  524288  2097152 ...
2:     5  20  80  320 1280  5120  20480  81920  327680 1310720  5242880 ...
3:    11  44 176  704 2816 11264  45056 180224  720896 2883584 11534336 ...
4:    14  56 224  896 3584 14336  57344 229376  917504 3670016 14680064 ...
5:    17  68 272 1088 4352 17408  69632 278528 1114112 4456448 17825792 ...
6:    23  92 368 1472 5888 23552  94208 376832 1507328 6029312 24117248 ...
7:    26 104 416 1664 6656 26624 106496 425984 1703936 6815744 27262976 ...
8:    29 116 464 1856 7424 29696 118784 475136 1900544 7602176 30408704 ...
9:    35 140 560 2240 8960 35840 143360 573440 2293760 9175040 36700160 ...
10:   38 152 608 2432 9728 38912 155648 622592 2490368 9961472 39845888 ...
...
----------------------------------------------------------------------------
The triangle t(n,k) begins:
k \ n  0   1   2    3    4     5     6      7      8      9 ...
---------------------------------------------------------------
1:     2
2:     5   8
3:    11  20  32
4:    14  44  80  128
5:    17  56 176  320  512
6:    23  68 224  704 1280  2048
7:    26  92 272  896 2816  5120  8192
8:    29 104 368 1088 3584 11264 20480  32768
9:    35 116 416 1472 4352 14336 45056  81920 131072
10:   38 140 464 1664 5888 17408 57344 180224 327680 524288
...
-----------------------------------------------------------------

Cf. A347834, A016789, A017617.
The rows k are given by -A000302 (for k=0), A004171, A003947(n+1), A002089, 2*A002042, ...
The columns n are given by 4^n*A347838 for n >= 0.

A := (n, k) -> 4^n*(3*(k + iquo(k, 3)) - 1):
for k from 1 to 10 do seq(A(n, k), n = 0..10) od;
# Alternatively:
gf  := n -> (4^n*((z*(z*(7*z + 3) + 3) - 1)))/((z - 1)^2*(1 + z + z^2)):
ser := n -> series(gf(n), z, 12):
col := (n, len) -> seq(coeff(ser(n), z, k), k = 1..len):
seq(print(col(n, 10)), n = 0..10); # Peter Luschny, Oct 26 2021

A[n_, k_] := 4^n (3(k + Quotient[k, 3]) - 1);
Table[A[n-k, k], {n, 1, 10}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Nov 07 2021, from Maple code *)

Array a:
a(k, n) = (3*A(k, n) + 1)/2, with the array A from A347834, for k >= 1, and n >= 0.
a(k, n) = 4^n*A347838(k) = 4^n*(2 + 3*k + 3*floor((k + 1)/3)).
Recurrence for rows k: a(k, n) = 4*a(k, n-1), for n >= 1, with a(k, 0) = A347838(k).
O.g.f.: expansion in z gives the o.g.f.s for rows k, also for k = 0: -A000302; expansion in x gives the o.g.f.s for columns n.
G(z, x) = (-1 + 3*z + 3*z^2 + 7*z^3)/((1 - z)*(1 - z^3)*(1 - 4*x)).
Triangle t:
t(k, n) = a(k-n, n), for k >= 1, and n = 0, 1, ..., k-1.

A175880 a(1)=1, a(2)=2. If n >= 3: if n/2 is in the sequence, a(n)=0, otherwise a(n)=n.

Original entry on oeis.org

1, 2, 3, 0, 5, 0, 7, 8, 9, 0, 11, 12, 13, 0, 15, 0, 17, 0, 19, 20, 21, 0, 23, 0, 25, 0, 27, 28, 29, 0, 31, 32, 33, 0, 35, 36, 37, 0, 39, 0, 41, 0, 43, 44, 45, 0, 47, 48, 49, 0, 51, 52, 53, 0, 55, 0, 57, 0, 59, 60, 61, 0, 63, 0, 65, 0, 67, 68, 69, 0, 71, 0, 73, 0, 75, 76, 77, 0, 79, 80

Offset: 1

Adriano Caroli, Dec 05 2010

If n > 0 and n is in the sequence, then a(2*n) = 0. Example: 5 is in the sequence, so a(2*5) = a(10) = 0.

Is this a(n) = n*A039982(n-1), n > 1? [R. J. Mathar, Dec 07 2010]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A053661.

A000040, A001749, A002001, A002042, A002063, A002089, A003947, A004171 and A081294 are subsequences.

import Data.List (delete)
a175880 n = a175880_list !! (n-1)
a175880_list = 1 : f [2..] [2..] where
   f (x:xs) (y:ys) | x == y    = x : (f xs $ delete (2*x) ys)
                   | otherwise = 0 : (f xs (y:ys))
for_bFile = take 10000 a175880_list
-- Reinhard Zumkeller, Feb 09 2011

A110654 := proc(n) 2*n+1-(-1)^n ; %/4 ;end proc:
A175880 := proc(n) if n <=2 then n; else if type(n,'even') then n-2*procname(A110654(n)) ; else n; end if; end if; end proc:
seq(A175880(n),n=1..40) ; # R. J. Mathar, Dec 07 2010

a(n) = n - (1 + (-1)^n) * a((2*n + 1 - (-1)^n)/4), n >= 3.

a(n) = n - A010673(n+1)*a(A110654(n)).

A179607 Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2x - 4x^2)/(1 - 2x - 8x^2).

Original entry on oeis.org

1, 4, 12, 56, 208, 864, 3392, 13696, 54528, 218624, 873472, 3495936, 13979648, 55926784, 223690752, 894795776, 3579117568, 14316601344, 57266143232, 229065097216, 916259340288, 3665039458304, 14660153638912, 58640622944256

Offset: 0

Johannes W. Meijer, Jul 28 2010

The a(n) represent the number of n-move routes of a fairy chess piece starting in the central square (m = 5) on a 3 X 3 chessboard. This fairy chess piece behaves like a king on the eight side and corner squares but on the central square the king goes crazy and turns into a red king, see A179596.
The sequence above corresponds to just one red king vector, i.e., A[5] vector, with decimal [binary] value 325 [1,0,1,0,0,0,1,0,1]. This vectors leads for the corner squares to A083424 and for the side squares to A003947.
The inverse binomial transform of A100284 (without the first leading 1).

Index entries for linear recurrences with constant coefficients, signature (2, 8).

Cf. A179597 (central square).

with(LinearAlgebra): nmax:=24; m:=5; A[1]:= [0,1,0,1,1,0,0,0,0]: A[2]:= [1,0,1,1,1,1,0,0,0]: A[3]:= [0,1,0,0,1,1,0,0,0]: A[4]:= [1,1,0,0,1,0,1,1,0]: A[5]:= [1,0,1,0,0,0,1,0,1]: A[6]:= [0,1,1,0,1,0,0,1,1]: A[7]:= [0,0,0,1,1,0,0,1,0]: A[8]:= [0,0,0,1,1,1,1,0,1]: A[9]:= [0,0,0,0,1,1,0,1,0]: A:=Matrix([A[1],A[2],A[3],A[4],A[5],A[6],A[7],A[8],A[9]]): for n from 0 to nmax do B(n):=A^n: a(n):= add(B(n)[m,k],k=1..9): od: seq(a(n), n=0..nmax);

Join[{1},LinearRecurrence[{2,8},{4,12},30]] (* Harvey P. Dale, Mar 01 2012 *)

G.f.: (1 + 2*x - 4*x^2)/(1 - 2*x - 8*x^2).
a(n) = 2*a(n-1) + 8*a(n-2), for n >= 3, with a(0) = 1, a(1) = 4 and a(2) = 12.
a(n) = 5*(4)^(n)/6 - (-2)^(n)/3 for n >= 1 and a(0) = 1.
a(n) = 4*A083424(n-1), n>0. - R. J. Mathar, Mar 08 2021

A135583 a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.

Original entry on oeis.org

3, 8, 28, 108, 428, 1708, 6828, 27308, 109228, 436908, 1747628, 6990508, 27962028, 111848108, 447392428, 1789569708, 7158278828, 28633115308, 114532461228, 458129844908, 1832519379628, 7330077518508, 29320310074028

Offset: 0

Paul Curtz, Feb 25 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A003947.

[(4+5*4^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 10 2011

NestList[4#-4&,3,30] (* or *) LinearRecurrence[{5,-4},{3,8},30] (* Harvey P. Dale, Feb 27 2013 *)

From R. J. Mathar, Mar 31 2008: (Start)
a(n) = (4 + 5*4^n)/3.
a(n) - a(n-1) = A003947(n).
O.g.f.: (3 - 7*x)/((1 - x)*(1 - 4*x)). (End)
a(0)=3, a(1)=8; for n>1, a(n) = 5*a(n-1) - 4*a(n-2). - Harvey P. Dale, Feb 27 2013
E.g.f.: (1/3)*(4*exp(x) + 5*exp(4*x)). - G. C. Greubel, Oct 20 2016

More terms from R. J. Mathar, Mar 31 2008

A163316 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1270, 5040, 20010, 79440, 315360, 1251930, 4969980, 19730070, 78325380, 310939920, 1234384470, 4900319640, 19453527810, 77227563240, 306581745960, 1217083163130, 4831636082580, 19180864497870, 76145131089180

Offset: 0

John Cannon and N. J. A. Sloane, Dec 03 2009

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, 3, -6).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6) )); // G. C. Greubel, May 12 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{3,3,3,3,-6}, {1,5,20,80,320,1270}, 30] (* G. C. Greubel, Dec 18 2016 *)
coxG[{5, 6, -3}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6)) \\ G. C. Greubel, Dec 18 2016

((1+x)*(1-x^5)/(1-4*x+9*x^5-6*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

a(n) = 3*a(n-1)+3*a(n-2)+3*a(n-3)+3*a(n-4)-6*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163878 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1280, 5110, 20400, 81450, 325200, 1298400, 5184000, 20697690, 82637820, 329940630, 1317324420, 5259563280, 20999387520, 83842374870, 334749945240, 1336526142210, 5336228292840, 21305481048360, 85064487085440

Offset: 0

John Cannon and N. J. A. Sloane, Dec 03 2009

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,-6).

a:=[5,20,80,320,1280,5110];; for n in [7..30] do a[n]:=3*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -6*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7) )); // G. C. Greubel, Aug 10 2019

seq(coeff(series((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 07 2017 *)
coxG[{6, 6, -3}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7)) \\ G. C. Greubel, Aug 07 2017

def A163878_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-4*t+9*t^6-6*t^7)).list()
A163878_list(30) # G. C. Greubel, Aug 10 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

a(n) = -6*a(n-6) + 3*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

A164354 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1280, 5120, 20470, 81840, 327210, 1308240, 5230560, 20912640, 83612160, 334295130, 1336566780, 5343813270, 21365442180, 85422543120, 341533342080, 1365506334720, 5459518355670, 21828050092440, 87272125451010

Offset: 0

John Cannon and N. J. A. Sloane, Dec 03 2009

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,-6).

a:=[5, 20, 80, 320, 1280, 5120, 20470];; for n in [8..30] do a[n]:=3*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -6*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-4*t+9*t^7-6*t^8) )); // G. C. Greubel, Aug 28 2019

seq(coeff(series((1+t)*(1-t^7)/(1-4*t+9*t^7-6*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019

coxG[{7,6,-3,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 01 2017 *)
CoefficientList[Series[(1+t)*(1-t^7)/(1-4*t+9*t^7-6*t^8), {t, 0, 30}], t] (* G. C. Greubel, Sep 15 2017 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-4*t+9*t^7-6*t^8)) \\ G. C. Greubel, Sep 15 2017

def A164354_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-4*t+9*t^7-6*t^8)).list()
A164354_list(30) # G. C. Greubel, Aug 28 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

a(n) = -6*a(n-7) + 3*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021

A165757 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310710, 5242800, 20971050, 83883600, 335532000, 1342118400, 5368435200, 21473587200, 85893734400, 343572480000, 1374280089690, 5497081037820, 21988166868630, 87952038348420

Offset: 0

John Cannon and N. J. A. Sloane, Dec 03 2009

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,3,3,3,-6).

a:=[5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310710];; for n in [11..30] do a[n]:=3*Sum([1..9], j-> a[n-j]) -6*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 17 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11) )); // G. C. Greubel, Sep 17 2019

seq(coeff(series((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 17 2019

CoefficientList[Series[(1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 07 2016 *)
coxG[{10, 6, -3}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 17 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11)) \\ G. C. Greubel, Sep 17 2019

def A165757_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-4*t+9*t^10-6*t^11)).list()
A165757_list(30) # G. C. Greubel, Sep 17 2019

G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

A166331 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242870, 20971440, 83885610, 335541840, 1342164960, 5368650240, 21474562560, 85898096640, 343591772160, 1374364631040, 5497448693760, 21989755453530, 87958864528380

Offset: 0

John Cannon and N. J. A. Sloane, Dec 03 2009

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,3,3,3,3,3,3,3,3,-6).

seq(coeff(series((1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 13 2020

CoefficientList[Series[(1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12), {t,0,30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{11, 6, -3}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 13 2020 *)

def A166331_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-4*t+9*t^11-6*t^12) ).list()
A166331_list(30) # G. C. Greubel, Mar 13 2020

G.f.: (t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(6*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).

cp's OEIS Frontend

A292540 Number of 3-cycles in the n-Sierpinski tetrahedron graph.

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A347839 An array of the positive integers congruent to 2 modulo 3 (A016789), read by antidiagonals upwards, giving the present triangle.

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A175880 a(1)=1, a(2)=2. If n >= 3: if n/2 is in the sequence, a(n)=0, otherwise a(n)=n.

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Haskell

Maple

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A179607 Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2*x - 4*x^2)/(1 - 2*x - 8*x^2).

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Maple

Mathematica

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A135583 a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.

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Magma

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Extensions

A163316 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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Magma

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PARI

Sage

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A163878 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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GAP

Magma

Maple

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A179607 Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2x - 4x^2)/(1 - 2x - 8x^2).