A000337 -id:A000337 - cp's OEIS frontend

A209359 a(n) = 2^n * (n^4 - 4n^3 + 18n^2 - 52*n + 75) - 75.

0, 1, 33, 357, 2405, 12405, 53877, 207541, 731829, 2411445, 7531445, 22523829, 64991157, 181977013, 496680885, 1326120885, 3473604533, 8947236789, 22706651061, 56869519285, 140755599285, 344683708341, 835954147253, 2009692372917, 4792831180725, 11346431180725

Offset: 0

Bruno Berselli, Mar 07 2012

This sequence is related to A036828 by the transform a(n) = n*A036828(n) - sum(A036828(i), i=0..n-1).

Bruno Berselli, Table of n, a(n) for n = 0..1000
B. Berselli, A description of the transform in Comments lines: website Matem@ticamente (in Italian).
Index entries for linear recurrences with constant coefficients, signature (11,-50,120,-160,112,-32).

Cf. A000079, A000337, A036826, A036828.

m:=25; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5)));

LinearRecurrence[{11, -50, 120, -160, 112, -32}, {0, 1, 33, 357, 2405, 12405}, 26]
Table[2^n(n^4-4n^3+18n^2-52n+75)-75,{n,0,30}] (* Harvey P. Dale, Mar 08 2023 *)

for(n=0, 25, print1(2^n*(n^4-4*n^3+18*n^2-52*n+75)-75", "));

G.f.: x*(1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5).

a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} k^4 * C(k,i). - Wesley Ivan Hurt, Sep 21 2017

A298011 If n = Sum_{i=1..h} 2^b_i with 0 <= b_1 < ... < b_h, then a(n) = Sum_{i=1..h} i * 2^b_i.

Original entry on oeis.org

0, 1, 2, 5, 4, 9, 10, 17, 8, 17, 18, 29, 20, 33, 34, 49, 16, 33, 34, 53, 36, 57, 58, 81, 40, 65, 66, 93, 68, 97, 98, 129, 32, 65, 66, 101, 68, 105, 106, 145, 72, 113, 114, 157, 116, 161, 162, 209, 80, 129, 130, 181, 132, 185, 186, 241, 136, 193, 194, 253, 196

Offset: 0

Rémy Sigrist, Jan 10 2018

This sequence is similar to A298043.

			For n = 42:
- 42 = 2 + 8 + 32,
- hence a(42) = 1*2 + 2*8 + 3*32 = 114.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Rémy Sigrist, Colored scatterplot of a(n) for n = 0..2^16 (where the color is function of A000120(n)).

Cf. A000120, A000337, A129760, A298043.

F[0]:= x -> x:
for i from 1 to 8 do
  F[i]:= unapply(convert(series(2*(x+1)*F[i-1](x^2)+H, x, 2^(i+1)),
    polynom), x)
od:
seq(coeff(F[8](x),x,j),j=0..2^9-1); # Robert Israel, Jan 16 2018

a[0] = 0; a[n_] := a[n] = If[OddQ[n], a[n - 1] + n, 2*a[n/2]]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

a(n) = my (b=binary(n), z=0); forstep (i=#b, 1, -1, if (b[i], b[i] = z++)); return (fromdigits(b, 2))

first(n) = n += (n-1)%2; my(res = vector(n)); res[1]= 1; for(i = 1, n\2, res[2 * i] = 2 * res[i]; res[2 * i + 1] = res[2 * i] + 2*i + 1); concat([0], res) \\ David A. Corneth, Jan 14 2018

a(n) = Sum_{k = 0..A000120(n)-1} A129760^k(n) for any n > 0 (where A129760^k denotes the k-th iterate of A129760).
a(n) >= n with equality iff n = 0 or n = 2^k for some k >= 0.
a(2 * n) = 2 * a(n).
a(2^n - 1) = A000337(n).
a(2 * n + 1) = a(2 * n) + 2 * n + 1. David A. Corneth, Jan 14 2018
G.f. g(x) satisfies g(x) = 2*(x+1)*g(x^2) + x*(1+x^2)/(1-x^2)^2. - Robert Israel, Jan 16 2018

A058394 A square array based on natural numbers (A000027) with each term being the sum of 2 consecutive terms in the previous row.

Original entry on oeis.org

1, 0, 1, 2, 1, 1, 0, 2, 2, 1, 3, 2, 3, 3, 1, 0, 3, 4, 5, 4, 1, 4, 3, 5, 7, 8, 5, 1, 0, 4, 6, 9, 12, 12, 6, 1, 5, 4, 7, 11, 16, 20, 17, 7, 1, 0, 5, 8, 13, 20, 28, 32, 23, 8, 1, 6, 5, 9, 15, 24, 36, 48, 49, 30, 9, 1, 0, 6, 10, 17, 28, 44, 64, 80, 72, 38, 10, 1, 7, 6, 11, 19, 32, 52, 80, 112, 129

Offset: 0

Henry Bottomley, Nov 24 2000

Changing the formula by replacing T(2n,0)=T(n,2) by T(2n,0)=T(n,m) for some other value of m, would make the generating function change to coefficient of x^n in expansion of (1+x)^k/(1-x^2)^m. This would produce A058393, A058395, A057884 (and effectively A007318).

			Rows are (1,0,2,0,3,0,4,...), (1,1,2,2,3,3,...), (1,2,3,4,5,6,...), (1,3,5,7,9,11,...), etc.

Rows are A027656 (A000027 with zeros), A008619, A000027, A005408, A008574 etc. Columns are A000012, A001477, A022856 etc. Diagonals include A034007, A045891, A045623, A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055251 etc. The triangle A055249 also appears in half of the array.

T(n, k)=T(n-1, k-1)+T(n, k-1) with T(0, k)=1, T(2n, 0)=T(n, 2) and T(2n+1, 0)=0. Coefficient of x^n in expansion of (1+x)^k/(1-x^2)^2.

A102029 Smallest semiprime with Hamming weight n (i.e., smallest semiprime with exactly n ones when written in binary), or -1 if no such number exists.

Original entry on oeis.org

4, 6, 14, 15, 55, 95, 247, 447, 511, 1535, 2047, 7167, 12287, 32255, 49151, 98303, 196607, 393215, 983039, 1572863, 3145727, 6291455, 8388607, 33423359, 50331647, 117440511, 201326591, 528482303, 805306367, 1879048191, 3221225471

Offset: 1

Jonathan Vos Post, Jun 23 2007

Semiprime analog of A061712. Extended by Stefan Steinerberger. Includes the subset Mersenne semiprimes A092561.

			a(1) = 4 because the first semiprime A001358(1) is 4 (base 10) which is written 100 in binary, the latter representation having exactly 1 one.
a(2) = 6 since A001358(2) = 6 = 110 (base 2) has exactly 2 ones.
a(4) = 15 since A001358(6) = 15 = 1111 (base 2) has exactly 4 ones and, as it also has no zeros, is the smallest of the Mersenne semiprimes.

Donovan Johnson, Table of n, a(n) for n = 1..250

Cf. A000043, A000120, A000337, A000668, A001358, A007088, A061712, A085724, A089226, A089998, A089999, A091991, A092558, A092559, A092561, A092562, A081093, A102782, A110472, A110699, A110700.

Join[{4},Table[SelectFirst[Sort[FromDigits[#,2]&/@Permutations[ Join[ PadRight[{}, n,1],{0}]]],PrimeOmega[#]==2&],{n,2,40}]] (* Harvey P. Dale, Feb 06 2015 *)

A108283 Triangle read by rows, generated from (..., 3, 2, 1).

Original entry on oeis.org

1, 1, 3, 1, 5, 6, 1, 7, 17, 10, 1, 9, 34, 49, 15, 1, 11, 57, 142, 129, 21, 1, 13, 86, 313, 547, 321, 28, 1, 15, 121, 586, 1593, 2005, 769, 36, 1, 17, 162, 985, 3711, 7737, 7108, 1793, 45, 1, 19, 209, 1534, 7465, 22461, 36409, 24604, 4097, 55, 1, 21, 262, 2257, 13539, 54121, 131836, 167481, 83653, 9217, 66

Offset: 1

Gary W. Adamson, May 30 2005

Inverse binomial transforms of each column form the rows of A108284. Rightmost diagonal = triangular numbers, (A000217); while diagonals going to the left from (1, 3, 6, ...) are A000337 starting with 1: (1, 5, 17, 49, ...); A014915: (1, 7, 34, 142, ...); A014916: (1, 9, 57, ...); A014917: (1, 11, 86, ...).

			4th column = 10, 49, 142, 313, ... = f(x), x = 1, 2, 3; 4x^3 + 3x^2 + 2x + 1. f(3) = 142.
First few rows of the triangle:
  1;
  1,  3;
  1,  5,  6;
  1,  7, 17,  10;
  1,  9, 34,  49,  15;
  1, 11, 57, 142, 129, 21;
  ...

Cf. A059045, A108284, A000217, A000337, A014915, A014916, A014917.

A108283 := proc(n,k)
    local x ;
    x := n-k+1 ;
    add( i*x^(i-1),i=1..k) ;
end proc:
seq(seq( A108283(n,k),k=1..n),n=1..10) ; # R. J. Mathar, Sep 14 2016

T[, 1] := 1; T[n, n_] := n (n + 1)/2; T[n_, k_] := (1 - (n - k + 1)^k*(k^2 - k*n + 1))/(n - k)^2; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 13 2016 *)

n-th column = f(x), x = 1, 2, 3; n*x^(n-1) + (n-1)*x^(n-2) + (n-3)*x^(n-3) + ... + 1.

T(n,k) = (1+ (n-k+1)^k*(n*k-k^2-1))/ (n-k)^2, n>k. - Jean-François Alcover, Sep 13 2016

More terms from Jean-François Alcover, Sep 13 2016

A127529 Triangle read by rows: T(n,k) is the number of ordered trees with n edges and jump-length equal to k (n >= 0, 0 <= k <= n-2).

Original entry on oeis.org

1, 1, 2, 4, 1, 8, 5, 1, 16, 17, 8, 1, 32, 49, 38, 12, 1, 64, 129, 141, 77, 17, 1, 128, 321, 453, 361, 143, 23, 1, 256, 769, 1326, 1399, 834, 247, 30, 1, 512, 1793, 3640, 4776, 3869, 1765, 402, 38, 1, 1024, 4097, 9539, 14911, 15353, 9722, 3469, 623, 47, 1, 2048, 9217

Offset: 0

Emeric Deutsch, Jan 18 2007

In the preorder traversal of an ordered tree, any transition from a node at a deeper level to a node on a strictly higher level is called a jump; the positive difference of the levels is called the jump distance; the sum of the jump distances in a given ordered tree is called the jump-length.
Rows 0 and 1 have one term each; row n (n >= 2) has n-1 terms.
Row sums are the Catalan numbers (A000108).
T(n,0) = A011782(n).
T(n,1) = A000337(n-2).
Sum_{k>=0} k*T(n,k) = binomial(2n-1, n-3) = A003516(n-1) for n >= 3.
The distribution of the statistic "number of jumps" is given in A091894. The average jump distance in all ordered trees with n edges is 2 - 5/(n+2) (i.e., about 2 levels for n large). The Krandick reference considers jump-length for full binary trees.
Also the number of Dyck n-paths with k valleys at height >= 1. - David Scambler, Sep 01 2011
Triangle T(n,k), with zeros omitted, given by (1,1,0,1,0,1,0,1,0,1,0,1,...) DELTA (0,0,1,0,1,0,1,0,1,0,1,0,1,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 06 2012

			Triangle starts:
   1;
   1;
   2;
   4,  1;
   8,  5,  1;
  16, 17,  8,  1;
  32, 49, 38, 12, 1;
Triangle (1,1,0,1,0,1,0,1,0,1, ...) DELTA (0,0,1,0,1,0,1,0,1,0,1,0,...) begins:
   1;
   1,   0;
   2,   0,   0;
   4,   1,   0,  0;
   8,   5,   1,  0,  0;
  16,  17,   8,  1,  0, 0;
  32,  49,  38, 12,  1, 0, 0;
  64, 129, 141, 77, 17, 1, 0, 0; ... - _Philippe Deléham_, Feb 06 2012

E. Deutsch, Dyck path enumeration, Discrete Math., 204, 1999, 167-202 (see Table 2).
FindStat - Combinatorial Statistic Finder, The number of valleys not on the x-axis of a Dyck path.
W. Krandick, Trees and jumps and real roots, J. Computational and Applied Math., 162, 2004, 51-55.

Cf. A000108, A000337, A003516, A011782, A091894.

G:=1/2/(1-2*z-t+t*z)*(-2*t+1+t*z-z+sqrt(-2*t*z+1-2*z+t^2*z^2-2*t*z^2+z^2)): Gser:=simplify(series(G,z=0,13)): for n from 0 to 12 do P[n]:=sort(coeff(Gser,z,n)) od: 1;1;for n from 2 to 12 do seq(coeff(P[n],t,j),j=0..n-2) od; # yields sequence in triangular form

n = 12; g[t_, z_] := 1/2/(1 - 2z - t + t*z)*(-2t + 1 + t*z - z + Sqrt[-2t*z + 1 - 2z + t^2*z^2 - 2t*z^2 + z^2]); Flatten[ CoefficientList[#, t]&  /@ CoefficientList[ Simplify[Series[g[t, z], {z, 0, n}]], z]] (* Jean-François Alcover, Jul 22 2011, after g.f. *)

T(n,m):=if n=0 and m=0 then 1 else if n=0 then 0 else sum(k*binomial(n,m+k)*binomial(n-k-1,m),k,0,n-m)/(n); /* Vladimir Kruchinin, Oct 29 2020 */

G.f.: G=G(t,z) satisfies (1 - t - 2*z + t*z)*G^2 - (1 - 2*t - z + t*z)*G - t = 0.

T(n,m) = Sum_{k=0..n-m} k*C(n,m+k)*C(n-k-1,m)/n, n>0, T(0,0)=1. - Vladimir Kruchinin, Oct 29 2020

A127983 a(n) = (n - 2/3)*2^n - n/2 + 3/4 - (-1)^n/12.

Original entry on oeis.org

1, 5, 18, 52, 137, 339, 808, 1874, 4263, 9553, 21158, 46416, 101029, 218447, 469668, 1004878, 2140835, 4543821, 9611938, 20272460, 42642081, 89478475, 187345568, 391468362, 816491167, 1700091209, 3534400158, 7337235784, 15211342493

Offset: 1

Artur Jasinski, Feb 09 2007

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000
W. Bosma, Signed bits and fast exponentiation, J. Th. des Nombres de Bordeaux Vol.13, Fasc. 1, 2001.
Index entries for linear recurrences with constant coefficients, signature (5,-7,-1,8,-4).

Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A073371, A000337.

[(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12: n in [1..50]]; // G. C. Greubel, May 08 2018

Table[(n-2/3)*2^n -n/2 +3/4 -(-1)^n/12, {n, 1, 50}]
LinearRecurrence[{5,-7,-1,8,-4}, {1,5,18,52,137}, 50] (* G. C. Greubel, May 08 2018 *)

a(n) = (n-2/3)*2^n -n/2 +3/4 -(-1)^n/12 \\ G. C. Greubel, May 08 2018

a(n) = (n - 2/3)*2^n - n/2 + 3/4 - (-1)^n/12.

G.f.: x*(1-2*x^3)/(1+x)/((2*x-1)^2*(x-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009 [checked and corrected by R. J. Mathar, Sep 16 2009]

A188716 a(n) = n + (n-1)*(2^n-2).

Original entry on oeis.org

1, 1, 4, 15, 46, 125, 316, 763, 1786, 4089, 9208, 20471, 45046, 98293, 212980, 458739, 983026, 2097137, 4456432, 9437167, 19922926, 41943021, 88080364, 184549355, 385875946, 805306345, 1677721576, 3489660903, 7247757286, 15032385509, 31138512868, 64424509411, 133143986146, 274877906913, 566935683040, 1168231104479

Offset: 0

Adeniji, Adenike and Samuel Makanjuola (somakanjuola(AT)unilorin.edu.ng) Apr 14 2011

Number of elements in the semigroup IDT_n.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Cf. A000337, A188377, A188947.

[n + (n-1)*(2^n-2): n in [0..50]]; // Vincenzo Librandi, May 01 2011

Table[n+(n-1)(2^n-2),{n,0,40}] (* or *) LinearRecurrence[{6,-13,12,-4},{1,1,4,15},40] (* Harvey P. Dale, Aug 03 2024 *)

a(n)=(n-1)<Charles R Greathouse IV, Apr 06 2012

From Colin Barker, Apr 06 2012: (Start)
a(n) = 6*a(n-1)-13*a(n-2)+12*a(n-3)-4*a(n-4).
G.f.: (1-5*x+11*x^2-8*x^3)/((1-x)^2*(1-2*x)^2). (End)
a(n) = A000337(n) - (n-1). - Andrew Penland , Mar 24 2016
E.g.f.: exp(x)*(2 - x + exp(x)*(2*x - 1)). - Stefano Spezia, Apr 10 2022

Edited by N. J. A. Sloane, Apr 23 2011

Offset changed from 1 to 0 by Vincenzo Librandi, May 01 2011

A193605 Triangle: (row n) = partial sums of partial sums of row n of Pascal's triangle.

Original entry on oeis.org

1, 1, 3, 1, 4, 8, 1, 5, 12, 20, 1, 6, 17, 32, 48, 1, 7, 23, 49, 80, 112, 1, 8, 30, 72, 129, 192, 256, 1, 9, 38, 102, 201, 321, 448, 576, 1, 10, 47, 140, 303, 522, 769, 1024, 1280, 1, 11, 57, 187, 443, 825, 1291, 1793, 2304, 2816, 1, 12, 68, 244, 630, 1268, 2116, 3084, 4097, 5120, 6144

Offset: 0

Clark Kimberling, Jul 31 2011

The n-th row is contains the partial sums of the n-th row of the array interpretation of A052509. - R. J. Mathar, Apr 22 2013

			First 5 rows of A193605:
1
1....3
1....4....8
1....5....12....20
1....6....17....32....48

Denis Neiter and Amsha Proag, Links Between Sums Over Paths in Bernoulli's Triangles and the Fibonacci Numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.8.3.

Cf. A193606.

A052509 := proc(n,k)
    if k = 0 then
        1;
    else
        procname(n,k-1)+binomial(n,k) ;
    end if;
end proc:
A193605 := proc(n,k)
    if k = 0 then
        1;
    else
        procname(n,k-1)+A052509(n,k) ;
    end if;
end proc: # R. J. Mathar, Apr 22 2013
# Alternative after Vladimir Kruchinin:
gf := ((x*y-1)/(1-2*x*y))^2/(1-x*y-x): ser := series(gf, x, 12):
p := n -> coeff(ser,x,n): row := n -> seq(coeff(p(n),y,k), k=0..n):
seq(row(n), n=0..10); # Peter Luschny, Aug 19 2019

u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}]
p[n_, k_] := Sum[u[n, h], {h, 0, k}]
Table[p[n, k], {n, 0, 12}, {k, 0, n}]
Flatten[%]   (* A193605 as a sequence *)
TableForm[Table[p[n, k], {n, 0, 12}, {k, 0, n}]]  (* A193605 as a triangle *)

T(n,k):=sum(((i+3)*2^(i-2))*binomial(n-i,k-i),i,1,min(n,k))+binomial(n,k);
/* Vladimir Kruchinin, Aug 20 2019 */

Writing the general term as T(n,k), for 0<=k<=n:
T(n,n)=A001792, T(n,n-1)=A001787, T(n,n-2)=A000337, T(n,n-3)=A045618.
T(n-1,k-1) + T(n-1,k) = T(n,k). - David A. Corneth, Oct 18 2016
G.f.: -(1-x*y)^2/(4*x^3*y^3+(4*x^3-8*x^2)*y^2+(5*x-4*x^2)*y+x-1). - Vladimir Kruchinin, Aug 19 2019
T(n,k) = C(n,k)+Sum_{i=1..n} (i+3)*2^(i-2)*C(n-i,k-i), - Vladimir Kruchinin, Aug 20 2019

More terms from David A. Corneth, Oct 18 2016

A241519 Denominators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0.

Original entry on oeis.org

1, 2, 2, 12, 3, 15, 60, 840, 105, 630, 630, 13860, 6930, 180180, 360360, 144144, 9009, 306306, 306306, 11639628, 14549535, 14549535, 58198140, 2677114440, 334639305, 3346393050

Offset: 0

Paul Curtz, Apr 24 2014

nonn

Generally, 2*b(n) = b(n-1) + f(n). See, for f(n)=n, A000337(n)/2^n.
a(0)=1. b(n) is mentioned in A241269.
Difference table of b(n):
     0,   1/2,   1/2,  5/12,    1/3,   4/15, ...
   1/2,     0, -1/12, -1/12,  -1/15,  -1/20, ...
  -1/2, -1/12,     0,  1/60,   1/60, 11/840, ...
  5/12,  1/12,  1/60,     0, -1/280, -1/280, ...
etc.
b(n) is mentioned in A241269 as an autosequence of the first kind.
The denominators of the first two upper diagonals are the positive Apéry numbers, A005430(n+1). Compare to the array in A003506.
Numerators: 0, 1, 1, 5, 1, 4, 13, 151, 16, 83, 73, 1433, 647, 15341, ... .

			0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ...
b(1) = (0+1)/2, hence a(1)=2.
b(2) = (1/2+1/2)/2 = 1/2, hence a(2)=2.
b(3) = (1/2+1/3)/2 = 5/12, hence a(3)=12.

Cf. A086466.

Cf. A242376 (numerators).

b[0] = 0; b[n_] := b[n] = 1/2*(b[n-1] + 1/n); Table[b[n] // Denominator, {n, 0, 25}] (* Jean-François Alcover, Apr 25 2014 *)
Table[-Re[LerchPhi[2, 1, n + 1]], {n, 0, 20}] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)
-Re[LerchPhi[2, 1, Range[20]]] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)
RecurrenceTable[{b[n] == b[n - 1]/2 + 1/(2 n), b[0] == 0}, b[n], {n, 20}] // Denominator (* Eric W. Weisstein, Dec 11 2017 *)

b(n) = -Re(Phi(2, 1, n + 1)) where Phi denotes the Lerch transcendent. - Eric W. Weisstein, Dec 11 2017

Extension, after a(13), from Jean-François Alcover, Apr 24 2014

cp's OEIS Frontend

A209359 a(n) = 2^n * (n^4 - 4*n^3 + 18*n^2 - 52*n + 75) - 75.

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A298011 If n = Sum_{i=1..h} 2^b_i with 0 <= b_1 < ... < b_h, then a(n) = Sum_{i=1..h} i * 2^b_i.

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A058394 A square array based on natural numbers (A000027) with each term being the sum of 2 consecutive terms in the previous row.

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A102029 Smallest semiprime with Hamming weight n (i.e., smallest semiprime with exactly n ones when written in binary), or -1 if no such number exists.

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A108283 Triangle read by rows, generated from (..., 3, 2, 1).

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Maple

Mathematica

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A127529 Triangle read by rows: T(n,k) is the number of ordered trees with n edges and jump-length equal to k (n >= 0, 0 <= k <= n-2).

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Maple

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Maxima

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A127983 a(n) = (n - 2/3)*2^n - n/2 + 3/4 - (-1)^n/12.

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Magma

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PARI

A209359 a(n) = 2^n * (n^4 - 4n^3 + 18n^2 - 52*n + 75) - 75.