A024206 -id:A024206 - cp's OEIS frontend

A082111 a(n) = n^2 + 5*n + 1.

1, 7, 15, 25, 37, 51, 67, 85, 105, 127, 151, 177, 205, 235, 267, 301, 337, 375, 415, 457, 501, 547, 595, 645, 697, 751, 807, 865, 925, 987, 1051, 1117, 1185, 1255, 1327, 1401, 1477, 1555, 1635, 1717, 1801, 1887, 1975, 2065, 2157, 2251, 2347, 2445, 2545, 2647

Offset: 0

Paul Barry, Apr 04 2003

From Gary W. Adamson, Jul 29 2009: (Start)
Let (a,b) = roots to x^2 - 5*x + 1 = 0 = 4.79128... and 0.208712...
Then a(n) = (n + a) * (n + b). Example: a(5) = 51 = (5 + 4.79128...) * (5 + 0.208712...) (End)
For n > 0: a(n) = A176271(n+2,n). - Reinhard Zumkeller, Apr 13 2010
a(n-2) = n*(n+1) - 5, n >= 0, with a(-2) = -5 and a(-1) = -3, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 21 for b = 2*n + 1. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - Wolfdieter Lang, Aug 15 2013
Numbers m > 0 such that 4m+21 is a square. - Bruce J. Nicholson, Jul 19 2017
Numbers represented as 151 in number base B. If 'digits' from B upwards are allowed then 151(2)=15, 151(3)=25, 151(4)=37, 151(5)=51 also. - Ron Knott, Nov 14 2017
If A and B are sequences satisfying the recurrence t(n) = 5*t(n-1) - t(n-2) with initial values A(0) = 1, A(1) = n+5 and B(0) = -1, B(1) = n, then a(n) = A(i)^2 - A(i-1)*A(i+1) = B(j)^2 - B(j-1)*B(j+1) for i, j > 0. - Klaus Purath, Oct 18 2020
The prime terms in this sequence are listed in A089376. The prime factors are given in A038893. With the exception of 3 and 7, each prime factor p divides exactly 2 out of any p consecutive terms. If a(i) and a(k) form such a pair that are divisible by p, then i + k == -5 (mod p). - Klaus Purath, Nov 24 2020

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

First row of A082110.

Cf. A002522, A014209, A028387, A028872, A338041.

Table[n^2 + 5*n + 1,{n,0,80}] (* Vladimir Joseph Stephan Orlovsky, Apr 19 2011 *)
LinearRecurrence[{3,-3,1},{1,7,15},80] (* Harvey P. Dale, Apr 22 2012 *)

a(n)=n^2+5*n+1 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n + a(n-1) + 4 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=7, a(2)=15. - Harvey P. Dale, Apr 22 2012
Sum_{n>=0} 1/a(n) = 8/15 + Pi*tan(sqrt(21)*Pi/2)/sqrt(21) = 1.424563592286456286... . - Vaclav Kotesovec, Apr 10 2016
From G. C. Greubel, Jul 19 2017: (Start)
G.f.: (1 + 4*x - 3*x^2)/(1 - x)^3.
E.g.f.: (x^2 + 6*x + 1)*exp(x). (End)
a(n) = A014209(n+1) - 2 = A338041(2*n+1). - Hugo Pfoertner, Oct 08 2020
a(n) = A249547(n+1) - A024206(n-4), n >= 5. - Klaus Purath, Nov 24 2020

New title (using given formula) from Hugo Pfoertner, Oct 08 2020

A163255 An interspersion: the order array of A163254.

Original entry on oeis.org

1, 3, 2, 7, 5, 4, 13, 10, 8, 6, 21, 17, 14, 11, 9, 31, 26, 22, 18, 15, 12, 43, 37, 32, 27, 23, 19, 16, 57, 50, 44, 38, 33, 28, 24, 20, 73, 65, 58, 51, 45, 39, 34, 29, 25, 91, 82, 74, 66, 59, 52, 46, 40, 35, 30, 111, 101, 92, 83, 75, 67, 60, 53, 47, 41, 36

Offset: 1

Clark Kimberling, Jul 24 2009

A permutation of the natural numbers.
Except for initial terms, rows 1 to 4 are A002061, A002522, A014206, A059100 and columns 1 to 4 are A002620, A024206, A014616, A004116.
This is the interspersion of the fractal sequence A167430; i.e., row n of this array consists of the numbers k such that n=A167430(k). - Clark Kimberling, Nov 03 2009

			Corner:
1....3....7...13
2....5...10...17
4....8...14...22
To obtain A163255 from A163254, replace each term of A163254 by its rank when all the terms of A163254 are arranged in increasing order.

Clark Kimberling, Doubly interspersed sequences, double interspersions and fractal sequences, The Fibonacci Quarterly 48 (2010) 13-20.

Cf. A002061, A002522, A014206, A059100, A002620, A024206, A014616, A004116, A163253, A163254.

Cf. A167430. [From Clark Kimberling, Nov 03 2009]

A181971 Triangle read by rows: T(n,0) = 1, T(n,n) = floor((n+3)/2) and T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 1, 4, 5, 3, 1, 5, 9, 8, 3, 1, 6, 14, 17, 11, 4, 1, 7, 20, 31, 28, 15, 4, 1, 8, 27, 51, 59, 43, 19, 5, 1, 9, 35, 78, 110, 102, 62, 24, 5, 1, 10, 44, 113, 188, 212, 164, 86, 29, 6, 1, 11, 54, 157, 301, 400, 376, 250, 115, 35, 6, 1, 12, 65, 211, 458, 701, 776, 626, 365, 150, 41, 7

Offset: 0

Reinhard Zumkeller, Jul 09 2012

Another variant of Pascal's triangle;
row sums: A081254; central terms: T(2*n,n) = A128082(n+1);
T(n,0) = 1;
T(n,1) = n + 1 for n > 0;
T(n,2) = A000096(n-1) for n > 1;
T(n,3) = A105163(n-2) for n > 2;
T(n,n-2) = A005744(n-1) for n > 1;
T(n,n-1) = A024206(n) for n > 0;
T(n,n) = A008619(n+1).

			The triangle begins:
.  0:                              1
.  1:                           1     2
.  2:                        1     3     2
.  3:                     1     4     5     3
.  4:                  1     5     9     8     3
.  5:               1     6    14    17    11     4
.  6:            1     7    20    31    28    15     4
.  7:         1     8    27    51    59    43    19     5
.  8:      1     9    35    78   110   102    62    24     5
.  9:   1    10    44   113   188   212   164    86    29     6.

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened
Index entries for triangles and arrays related to Pascal's triangle

Cf. A035317, A007318, A074909.

a181971 n k = a181971_tabl !! n !! k
a181971_row n = a181971_tabl !! n
a181971_tabl = map snd $ iterate f (1, [1]) where
   f (i, row) = (1 - i, zipWith (+) ([0] ++ row) (row ++ [i]))

T[n_ /; n >= 0, k_ /; k >= 0] := T[n, k] = If[n == k, Quotient[n + 3, 2], If[k == 0, 1, If[n > k, T[n - 1, k - 1] + T[n - 1, k]]]];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Oct 12 2021 *)

{T(n,k)=if(n==k,(n+3)\2,if(k==0,1,if(n>k,T(n-1,k-1)+T(n-1,k))))}
for(n=0,12,for(k=0,n,print1(T(n,k),","));print("")) \\ Paul D. Hanna, Jul 18 2012

A055609 Number of 3 X n binary matrices with no zero rows or columns, up to row and column permutation.

Original entry on oeis.org

1, 5, 17, 42, 91, 180, 328, 565, 930, 1470, 2248, 3344, 4849, 6881, 9579, 13104, 17649, 23442, 30736, 39833, 51074, 64842, 81574, 101766, 125959, 154771, 188883, 229044, 276085, 330926, 394558, 468083, 552696, 649692, 760482, 886602, 1029691, 1191539, 1374065, 1579326

Offset: 1

Vladeta Jovovic, Jun 03 2000

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3, -1, -3, -1, 3, 6, -6, -3, 1, 3, 1, -3, 1).

Column k=3 of A056152.

Cf. A024206, A002623, A002727.

Vec((G(3, x) - G(2, x))*(1 - x) + O(x^30)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023

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

Terms a(37) and beyond from Andrew Howroyd, Mar 25 2020

A267019 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any northeast or northwest neighbors modulo n and the upper left element equal to 0.

Original entry on oeis.org

1, 1, 1, 1, 3, 2, 1, 10, 5, 6, 1, 35, 15, 8, 24, 1, 126, 59, 21, 11, 120, 1, 462, 257, 137, 45, 15, 720, 1, 1716, 1205, 759, 259, 37, 19, 5040, 1, 6435, 5879, 4835, 2063, 537, 147, 24, 40320, 1, 24310, 29693, 31591, 18157, 5493, 1015, 62, 29, 362880, 1, 92378, 153097

Offset: 1

R. H. Hardin, Jan 09 2016

Table starts
......1..1...1....1......1........1.........1.........1..........1..........1
......1..3..10...35....126......462......1716......6435......24310......92378
......2..5..15...59....257.....1205......5879.....29693.....153097.....806375
......6..8..21..137....759.....4835.....31591....216460....1516047...10864196
.....24.11..45..259...2063....18157....172169...1717333...17555313..184061791
....120.15..37..537...5493....69265....912057..13122646..193577805.2965487933
....720.19.147.1015..15171...255437...4893787.100710495.2166450939
...5040.24..62.2132..39804...997598..26320280.787556232
..40320.29.537.4045.117871..3689017.143694547
.362880.35.104.8511.292196.14484099

			Some solutions for n=4 k=4
..0..2..3..2....0..1..3..2....0..1..3..2....0..3..1..2....0..3..0..2
..2..0..2..0....2..0..2..0....2..0..2..0....3..1..3..1....3..1..3..1
..1..3..1..3....1..3..1..3....0..3..1..2....2..0..2..0....2..0..1..3
..0..1..3..1....3..2..0..1....3..1..3..1....0..2..1..3....1..2..0..2

R. H. Hardin, Table of n, a(n) for n = 1..126

Column 1 is A000142(n-1).
Column 2 is A024206(n+1).
Row 2 is A001700(n-1).
Row 3 is A266682.

A055192 Number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block, up to isomorphism.

Original entry on oeis.org

1, 2, 5, 12, 35, 108, 393, 1666, 8543, 54190, 436740, 4565450, 62930604, 1156277748, 28509174012, 946786816168, 42448800498744, 2573207315483554, 211180300735118954, 23490473719472829824, 3545759835559406756008, 727077827560669587718290

Offset: 2

Vladeta Jovovic, Jun 18 2000

nonn

Also the number of connected split graphs on n vertices (cf. A048194). - Falk Hüffner, Dec 01 2015

Inverse Euler transform is A007776. - Andrew Howroyd, Oct 03 2018

Alois P. Heinz, Table of n, a(n) for n = 2..40

Equals second differences of A049312.
Cf. A007776, A024206, A055609, A055082, A055083, A055084.
Row sums of A056152 and also of A122083.

b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Flatten @ Table[ Map[ Function[{p}, p + j*x^i], b[n - i*j, i - 1]], {j, 0, n/i}]]];
g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}];
A[n_, k_] := g[Min[n, k], Abs[n - k]];
A049312[d_] := Sum[A[n, d - n], {n, 0, d}];
Differences[Table[A049312[n], {n, 0, 23}], 2] (* Jean-François Alcover, Sep 05 2019, after Alois P. Heinz in A049312 *)

A108279 a(n) = number of squares with corners on an n X n grid, distinct up to congruence.

Original entry on oeis.org

0, 1, 3, 5, 8, 11, 15, 18, 23, 28, 33, 38, 45, 51, 58, 65, 73, 80, 89, 97, 107, 116, 126, 134, 146, 158, 169, 180, 192, 204, 218, 228, 243, 257, 270, 285, 302, 316, 331, 346, 364, 379, 397, 414, 433, 451, 468, 484, 505, 523, 544, 563, 584, 603, 625

Offset: 1

Hugo Pfoertner, Jun 05 2005

nonn

Number of different sizes occurring among the A002415(n) = n^2*(n^2-1)/12 squares that can be drawn using points of an n X n square array as corners.

a(n) is also the number of rectangular isosceles triangles, distinct up to congruence, on an n X n grid (or geoboard). - Martin Renner, May 03 2011

			a(3)=3 because the 6 different squares that can be drawn on a 3 X 3 square lattice come in 3 sizes:
  4 squares of side length 1:
  x.x.o    o.x.x    o.o.o    o.o.o
  x.x.o    o.x.x    x.x.o    o.x.x
  o.o.o    o.o.o    x.x.o    o.x.x
  1 square of side length sqrt(2):
  o.x.o
  x.o.x
  o.x.o
  1 square of side length 2:
  x.o.x
  o.o.o
  x.o.x
.
a(4)=5 because there are 5 different sizes of squares that can be drawn using the points of a 4 X 4 square lattice:
  x.x.o.o    o.x.o.o    x.o.x.o    o.x.o.o    x.o.o.x
  x.x.o.o    x.o.x.o    o.o.o.o    o.o.o.x    o.o.o.o
  o.o.o.o    o.x.o.o    x.o.x.o    x.o.o.o    o.o.o.o
  o.o.o.o    o.o.o.o    o.o.o.o    o.o.x.o    x.o.o.x

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Henry Bottomley, Illustration of initial terms of A002415

Cf. A002415, A024206, A187452.

a[n_] := Module[{v = Table[0, (n - 1)^2]}, Do[v[[k^2 + (w - k)^2]] = 1, {w, 1, n - 1}, {k, 0, w - 1}]; Total[v]]; Array[a, 55](* Jean-François Alcover, Oct 08 2017, after Andrew Howroyd *)

a(n) = my(v=vector((n-1)^2)); for(w=1, n-1, for(k=0, w-1, v[k^2+(w-k)^2]=1)); vecsum(v); \\ Andrew Howroyd, Sep 17 2017

More terms from David W. Wilson, Jun 07 2005

A056152 Triangular array giving number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block with k=1..n-1 vertices, up to isomorphism.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 17, 8, 1, 1, 11, 42, 42, 11, 1, 1, 15, 91, 179, 91, 15, 1, 1, 19, 180, 633, 633, 180, 19, 1, 1, 24, 328, 2001, 3835, 2001, 328, 24, 1, 1, 29, 565, 5745, 20755, 20755, 5745, 565, 29, 1, 1, 35, 930, 15274, 102089, 200082, 102089

Offset: 2

Vladeta Jovovic, Jul 29 2000

Also table read by rows: for 0 < k < n, a(n, k) = number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block with k vertices, up to isomorphism.
a(n, k) is the number of isomorphism classes of finite subdirectly irreducible almost distributive lattices in which the N-quotient has k upper covers and (n - k) lower covers. - David Wasserman, Feb 11 2002
Also, row n gives the number of unlabeled bicolored graphs having k nodes of one color and n-k nodes of the other color, with no isolated nodes; the color classes are not interchangeable.

			Triangle begins:
  1;
  1,  1;
  1,  3,   1;
  1,  5,   5,   1;
  1,  8,  17,   8,  1;
  1, 11,  42,  42,  11,  1;
  1, 15,  91, 179,  91,  15,  1;
  1, 19, 180, 633, 633, 180, 19, 1;
  ...
There are 17 bipartite graphs with 6 vertices, no isolated vertices and a distinguished bipartite block with 3 vertices, or equivalently, there are 17 3 X 3 binary matrices with no zero rows or columns, up to row and column permutation:
[0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 0 1] [0 1 0] [0 1 0] [0 1 0] [0 1 1] [0 1 1] [0 1 1] [1 1 0]
[1 1 0] [1 1 1] [1 0 0] [1 0 1] [1 1 1] [1 0 1] [1 1 0] [1 1 1] [1 1 0]
and
[0 0 1] [0 0 1] [0 1 1] [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1 1 1]
[1 1 0] [1 1 1] [0 1 1] [0 1 1] [1 0 1] [1 0 1] [1 1 1] [1 1 1]
[1 1 1] [1 1 1] [1 0 1] [1 1 1] [1 1 0] [1 1 1] [1 1 1] [1 1 1].

J. G. Lee, Almost Distributive Lattice Varieties, Algebra Universalis, 21 (1985), 280-304.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning, B 5 (1978), 31-43. See Table 2.
F. Harary, L. March and R. W. Robinson, On enumerating certain design problems in terms of bicolored graphs with no isolates, Environment and Planning B: Urban Analytics and City Science, 5 (1978), 31-43. [Annotated scanned copy] See Table 2.

Columns k=1..6 are A000012, A024206, A055609, A055082, A055083, A055084.
Row sums give A055192.
See A122083 for another version of this triangle.
Cf. A049312, A048194, A028657, A049311.

A112970 A generalized Stern sequence.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 2, 2, 1, 5, 3, 3, 2, 5, 2, 3, 1, 6, 4, 3, 2, 6, 2, 3, 1, 7, 5, 4, 3, 8, 3, 5, 2, 8, 5, 4, 2, 8, 3, 3, 1, 9, 6, 5, 4, 9, 3, 6, 2, 9, 6, 4, 2, 9, 3, 3, 1, 10, 7, 6, 5, 11, 4, 8, 3, 12, 8, 6, 3, 13, 5, 5, 2, 13, 8, 7, 5, 12, 4, 7, 2, 12, 8, 5, 3, 11, 3, 4, 1, 12, 9, 7, 6

Offset: 0

Paul Barry, Oct 07 2005

Conjectures: a(2^n)=a(2^(n+1)+1)=A033638(n); a(2^n-1)=a(3*2^n-1)=1.

The Gi1 and Gi2 triangle sums, see A180662 for their definitions, of Sierpinski's triangle A047999 equal this sequence. The Gi1 and Gi2 sums can also be interpreted as (i + 4*j = n) and (4*i + j = n) sums, see the Northshield reference. Some A112970(2^n-p) sequences, 0<=p<=32, lead to known sequences, see the crossrefs. - Johannes W. Meijer, Jun 05 2011

Sam Northshield, Sums across Pascal's triangle modulo 2, Congressus Numerantium, 200, pp. 35-52, 2010. - _Johannes W. Meijer_, Jun 05 2011

Cf. A002487, A112971.
Cf. A120562 (Northshield).
Cf. A033638 (p=0), A000012 (p=1), A004526 (p=2, p=3, p=5, p=9, p=17), A002620 (p=4, p=7, p=13, p=25), A000027 (p=6, p=11, p=21), A004116 (p=8, p=15, p=29), A035106 (p=10, p=19), A024206 (p=14, p=27), A007494 (p=18), A014616 (p=22), A179207 (p=26). - Johannes W. Meijer, Jun 05 2011

A112970:=proc(n) option remember; if n <0 then A112970(n):=0 fi: if (n=0 or n=1) then 1 elif n mod 2 = 0 then A112970(n/2) + A112970((n/2)-2) else A112970((n-1)/2); fi; end: seq(A112970(n),n=0..99); # Johannes W. Meijer, Jun 05 2011

a[n_] := a[n] = Which[n<0, 0, n==0 || n==1, 1, Mod[n, 2]==0, a[n/2] + a[n/2-2], True, a[(n-1)/2]];
Table[a[n], {n, 0, 99}] (* Jean-François Alcover, Aug 02 2022 *)

a(n) = Sum_{k=0..n} mod(sum{j=0..n, (-1)^(n-k)*C(j, n-j)*C(k, j-k)}, 2).
From Johannes W. Meijer, Jun 05 2011: (Start)
a(2*n+1) = a(n) and a(2*n) = a(n) + a(n-2) with a(0) = 1, a(1) = 1 and a(n)=0 for n<=-1.
G.f.: Product_{n>=0} (1 + x^(2^n) + x^(4*2^n)). (End)
G.f. A(x) satisfies: A(x) = (1 + x + x^4) * A(x^2). - Ilya Gutkovskiy, Jul 09 2019

A267751 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any north neighbor modulo n and the upper left element equal to 0.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 10, 5, 1, 1, 35, 39, 8, 1, 1, 126, 357, 118, 11, 1, 1, 462, 3471, 2386, 313, 15, 1, 1, 1716, 35003, 54956, 13451, 780, 19, 1, 1, 6435, 362265, 1350674, 679735, 68151, 1789, 24, 1, 1, 24310, 3821877, 34568612, 37668275, 7280046, 314491, 4024

Offset: 1

R. H. Hardin, Jan 20 2016

Table starts
.1..1....1.......1........1.........1............1............1...........1
.1..3...10......35......126.......462.........1716.........6435.......24310
.1..5...39.....357.....3471.....35003.......362265......3821877....40918431
.1..8..118....2386....54956...1350674.....34568612....910791802.24537293344
.1.11..313...13451...679735..37668275...2218059985.136270559675
.1.15..780...68151..7280046.873319806.113187903900
.1.19.1789..314491.69784981
.1.24.4024.1381976
.1.29.8793
.1.35

			Some solutions for n=4 k=4
..0..0..1..2....0..2..3..0....0..3..1..2....0..0..2..3....0..1..2..0
..1..0..2..2....1..2..3..0....0..3..2..3....1..1..2..3....0..1..3..1
..2..1..3..3....1..3..0..1....1..3..2..0....2..1..3..3....1..2..3..2
..3..1..3..0....2..3..1..2....1..0..2..1....2..1..0..0....2..3..0..3

R. H. Hardin, Table of n, a(n) for n = 1..72

Diagonal is A267624.
Column 2 is A024206(n+1).
Row 2 is A001700(n-1).
Row 3 is A266456.

cp's OEIS Frontend

A082111 a(n) = n^2 + 5*n + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A163255 An interspersion: the order array of A163254.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A181971 Triangle read by rows: T(n,0) = 1, T(n,n) = floor((n+3)/2) and T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

A055609 Number of 3 X n binary matrices with no zero rows or columns, up to row and column permutation.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

Extensions

A267019 T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with every element equal to or 1 greater than any northeast or northwest neighbors modulo n and the upper left element equal to 0.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A055192 Number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block, up to isomorphism.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A108279 a(n) = number of squares with corners on an n X n grid, distinct up to congruence.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A056152 Triangular array giving number of bipartite graphs with n vertices, no isolated vertices and a distinguished bipartite block with k=1..n-1 vertices, up to isomorphism.

Views

Author

Keywords

Comments

Examples

References

Links