A055809 -id:A055809 - cp's OEIS frontend

A055203 Number of different relations between n intervals on a line.

1, 1, 13, 409, 23917, 2244361, 308682013, 58514835289, 14623910308237, 4659168491711401, 1843200116875263613, 886470355671907534969, 509366445167037318008557, 344630301458257894126724041, 271188703889907190388528763613, 245570692377888837925941696215449

Offset: 0

Sylviane R. Schwer (schwer(AT)lipn.univ-paris13.fr), Jun 22 2000

From Peter Bala, Jan 30 2018: (Start)
Number of alignments of n strings of length 2 (see Slowinski).
Conjectures: a(n) == 1 (mod 12); for fixed k, the sequence a(n) (mod k) eventually becomes periodic with exact period a divisor of phi(k), where phi(k) is Euler's totient function A000010. (End)

			In case n = 2 this is the Delannoy number a(2) = D(2,2) = 13.
a(2) = 13 because if you have two intervals [a1,a2] and [b1,b2], using a for a1 or a2 and b for b1 or b2 and writing c if an a is at the same place as a b, we get the following possibilities: aabb, acb, abab, cab, abc, baab, abba, cc, bac, cba, baba, bca, bbaa.

S. R. Schwer, Dépendances temporelles: les mots pour le dire, Journées Intelligence Artificielle, 1998.
S. R. Schwer, Enumerating and generating Allen's algebra, in preparation.

T. D. Noe, Table of n, a(n) for n = 0..100
Tim Fernando and Carl Vogel, Prior Probabilities of Allen Interval Relations over Finite Orders, 11th International Conference on Agents and Artificial Intelligence (NLPinAI 2019) Prague.
IBM Ponder This, Jan 01 2001
J. B. Slowinski, The Number of Multiple Alignments, Molecular Phylogenetics and Evolution 10:2 (1998), 264-266. doi:10.1006/mpev.1998.0522
Peter Stockman, Upper Bounds on the Time Complexity of Temporal CSPs, Linköping University | Department of Computer science, Master's thesis, 30 ECTS | Datateknik 2016 | LIU-IDA/LITH-EX-A--16/022--SE.
David Adam Woods, Strings for Temporal Annotation and Semantic Representation of Events, Ph. D. Dissertation, Univ. of Dublin, Trinity College (Ireland, 2022).

Cf. A035317, A055809, A055810, A078739, A122193, A062208.

Row n=2 of A262809.

lambda := proc(p,n) option remember; if n = 1 then if p = 2 then RETURN(1) else RETURN(0) fi; else RETURN((p*(p-1)/2)*(lambda(p,n-1)+2*lambda(p-1,n-1)+lambda(p-2,n-1))) fi; end; A055203 := n->add(lambda(i,n),i=2..2*n);
A055203 := proc(n) local k; add(A078739(n,k)*k!,k=0..2*n)/2^n end:
seq(A055203(n),n=0..15); # Peter Luschny, Mar 25 2011
# second Maple program:
b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-j)*binomial(n, j), j=1..n))
    end:
a:= n-> ceil(add(b(n+k)*binomial(n, k), k=0..n)/2^(n+1)):
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 10 2018

a[n_] := Sum[((m-1)*m)^n / 2^(m+n+1), {m, 0, Infinity}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Oct 10 2011, after Vladeta Jovovic *)
With[{r = 2}, Flatten[{1, Table[Sum[Sum[(-1)^i*Binomial[j, i]*Binomial[j - i, r]^k, {i, 0, j}], {j, 0, k*r}], {k, 1, 15}]}]] (* Vaclav Kotesovec, Mar 22 2016 *)

a(n) = Sum_{i=2..2n} lambda(i, n), with lambda(p, 1) = 1 if p = 2, otherwise 0; lambda(p, n) = (p*(p-1)/2)*(lambda(p, n-1) + 2*lambda(p-1, n-1) + lambda(p-2, n-1)).
lambda(p, n) = Sum_k[( - 1)^(p + k) * C(p, k) * ((k - 1)*k/2)^n]. So if T(m, 0), T(m, 1), ..., T(m, m) is any row of A035317 with m >= 2n - 1 then a(n) = Sum_j[(-1)^j * T(m, j) * ((m - j + 1)*(m - j)/2)^n]; e.g., a(2) = 13 = 1*6^2 - 3*3^2 + 4*1^2 - 2*0^2 = 1*10^2 - 4*6^2 + 7*3^2 - 6*1^2 + 3*0^2 = 1*15^2 - 5*10^2 + 11*6^2 - 13*3^2 + 9*1^2 - 3*0^2 etc. while a(3) = 409 = 1*15^3 - 5*10^3 + 11*6^3 - 13*3^3 + 9*1^3 - 3*0^3 etc. - Henry Bottomley, Jan 03 2001
Row sums of A122193. - Vladeta Jovovic, Aug 24 2006
a(n) = Sum_{k=0..n} k!*Stirling2(n,k)*A121251(k). - Vladeta Jovovic, Aug 25 2006
E.g.f.: Sum_{m>=0} exp(x*binomial(m,2))/2^(m+1). - Vladeta Jovovic, Sep 24 2006
a(n) = Sum_{m>=0} binomial(m,2)^n/2^(m+1). - Vladeta Jovovic, Aug 17 2006
a(n) = (1/2^n)*Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A000670(n+k). - Vladeta Jovovic, Aug 17 2006
a(n) ~ n! * n^n * 2^(n-1) / (exp(n) * (log(2))^(2*n+1)). - Vaclav Kotesovec, Mar 15 2014
From Peter Bala, Jan 30 2018: (Start)
a(n) = Sum_{k = 2..2*n} Sum_{i = 0..k} (-1)^(k-i)*binomial(k,i)*(i*(i-1)/2)^n.
a(n) = (1/2^(n+1))*Sum_{k = 0..n} binomial(n,k)*A000670(n+k) for n >= 1. (End)

More terms from Larry Reeves (larryr(AT)acm.org), Oct 04 2000

More terms from N. J. A. Sloane, Jan 03 2001

A062109 Expansion of ((1-x)/(1-2*x))^4.

Original entry on oeis.org

1, 4, 14, 44, 129, 360, 968, 2528, 6448, 16128, 39680, 96256, 230656, 546816, 1284096, 2990080, 6909952, 15859712, 36175872, 82051072, 185139200, 415760384, 929562624, 2069889024, 4591714304, 10150215680, 22364028928, 49123688448, 107592286208, 235015241728, 512040632320

Offset: 0

Henry Bottomley, May 30 2001

If X_1,X_2,...,X_n are 2-blocks of a (2n+4)-set X then, for n >= 1, a(n+1) is the number of (n+3)-subsets of X intersecting each X_i, (i=1,2,...,n). - Milan Janjic, Nov 23 2007
If the offset here is set to zero, the binomial transform of A006918. - R. J. Mathar, Jun 29 2009
a(n) is the number of weak compositions of n with exactly 3 parts equal to 0. - Milan Janjic, Jun 27 2010
Binomial transform of A002623. - Carl Najafi, Jan 22 2013
Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)^4; see A291000. - Clark Kimberling, Aug 24 2017

Harry J. Smith, Table of n, a(n) for n = 0..200
Robert Davis and Greg Simay, Further Combinatorics and Applications of Two-Toned Tilings, arXiv:2001.11089 [math.CO], 2020.
Nickolas Hein and Jia Huang, Variations of the Catalan numbers from some nonassociative binary operations, arXiv:1807.04623 [math.CO], 2018.
Milan Janjic, Two Enumerative Functions
Milan Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 13 2013
Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(((1-x)/(1-2*x))^4)); // G. C. Greubel, Oct 16 2018

seq(coeff(series(((1-x)/(1-2*x))^4, x,n+1),x,n),n=0..30); # Muniru A Asiru, Jul 01 2018

CoefficientList[Series[(1 - x)^4/(1 - 2 x)^4, {x, 0, 26}], x] (* Michael De Vlieger, Jul 01 2018 *)
LinearRecurrence[{8,-24,32,-16},{1,4,14,44,129},30] (* Harvey P. Dale, Sep 02 2022 *)

a(n)=if(n<1,n==0,(n+5)*(n^2+13*n+18)*2^n/96)

a(n) = (n+5)*(n^2 + 13*n + 18)*2^(n-5)/3, with a(0)=1.
a(n) = A055809(n-5)*2^(n-4).
a(n) = 2*a(n-1) + A058396(n) - A058396(n-1).
a(n) = Sum_{kA058396(n).
a(n) = A062110(4, n).
G.f.: (1-x)^4/(1-2*x)^4.

A055807 Triangle T read by rows: T(i,j) = R(i-j,j), where R(i,0) = 1 for i >= 0, R(0,j) = 0 for j >= 1, and R(i,j) = Sum_{h=0..i-1, k=0..j} R(h,k) for i >= 1 and j >= 1.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 7, 4, 1, 0, 1, 15, 12, 5, 1, 0, 1, 31, 32, 18, 6, 1, 0, 1, 63, 80, 56, 25, 7, 1, 0, 1, 127, 192, 160, 88, 33, 8, 1, 0, 1, 255, 448, 432, 280, 129, 42, 9, 1, 0, 1, 511, 1024, 1120, 832, 450, 180, 52, 10, 1, 0, 1, 1023

Offset: 0

Clark Kimberling, May 28 2000

Formatted as a triangular array, it is [1, 0, 1, 1, 0, 0, 0, 0, 0, ...] DELTA [0, 1, 0, -1, 1, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 05 2006

The square array (R(n,k): n,k >= 0) referred to in the name of the sequence is actually A050143. - Petros Hadjicostas, Feb 13 2021

			Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
  1;
  1,   0;
  1,   1,   0;
  1,   3,   1,   0;
  1,   7,   4,   1,   0;
  1,  15,  12,   5,   1,   0;
  1,  31,  32,  18,   6,   1,  0;
  1,  63,  80,  56,  25,   7,  1, 0;
  1, 127, 192, 160,  88,  33,  8, 1, 0;
  1, 255, 448, 432, 280, 129, 42, 9, 1, 0;
  ...
Florez et al. (2019) give the triangle in this form:
    1,    0,    0,   0,   0,   0,  0,  0, 0, ...
    3,    1,    0,   0,   0,   0,  0,  0, 0, ...
    7,    4,    1,   0,   0,   0,  0,  0, 0, ...
   15,   12,    5,   1,   0,   0,  0,  0, 0, ...
   31,   32,   18,   6,   1,   0,  0,  0, 0, ...
   63,   80,   56,  25,   7,   1,  0,  0, 0, ...
  127,  192,  160,  88,  33,   8,  1,  0, 0, ...
  255,  448,  432, 280, 129,  42,  9,  1, 0, ...
  511, 1024, 1120, 832, 450, 180, 52, 10, 1, ...
  ...

G. C. Greubel, Rows n = 0..100 of triangle, flattened
Rigoberto Flórez, Leandro Junes, and José L. Ramírez, Enumerating several aspects of non-decreasing Dyck paths, Discrete Mathematics Vol. 342, Issue 11 (2019), 3079-3097. See page 3091. Gives the triangle in a slightly different form (see the Examples section).
Clark Kimberling, Path-counting and Fibonacci numbers, Fib. Quart. 40(4) (2002) 328-338, Example 3A.

Rows sums: A001519 (odd-indexed Fibonacci numbers).
Cf. A050143, A050147, A050148, A111516.
Cf. A055809, A055810, A055811, A055815, A055816, A055817.

T:= function(i,j)
    if j=0 then return 1;
    elif i=0 then return 0;
    else return Sum([0..i-1], h-> Sum([0..j], m-> T(h,m) ));
    fi; end;
Flat(List([0..12], n-> List([0..n], k-> T(n-k,k) ))); # G. C. Greubel, Jan 23 2020

function T(i,j)
  if j eq 0 then return 1;
  elif i eq 0 then return 0;
  else return (&+[(&+[T(h,m): m in [0..j]]): h in [0..i-1]]);
  end if; return T; end function;
[T(n-k,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 23 2020

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
      fi; end:
seq(seq(T(n-k, k), k=0..n), n=0..12); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n-k, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Jan 23 2020 *)

T(i,j) = if(j==0, 1, if(i==0, 0, sum(h=0,i-1, sum(m=0,j, T(h,m) ))));
for(n=0,12, for(k=0, n, print1(T(n-k,k), ", "))) \\ G. C. Greubel, Jan 23 2020

@CachedFunction
def T(i, j):
    if j==0: return 1
    elif i==0: return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[[T(n-k, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 23 2020

T(2*n,n) = A050146(n).
G.f.: (1-2*x)*(1-x*y)/((1-x)*(1-x*y-2*x+x^2*y)). - R. J. Mathar, Aug 11 2015
From Petros Hadjicostas, Feb 13 2021: (Start)
T(n,k) = A050143(n-k, k) for 0 <= k <= n.
T(n,k) = (n-k)*hypergeom([-n + k + 1, k], [2], -1) = Sum_{s=1..n-k} binomial(n-k,s)*binomial(s+k-2,k-1) for 1 <= k <= n.
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) for 2 <= k <= n-1 with initial conditions T(n,0) = 1 for n >= 0, T(n,n) = 0 for n >= 1, and T(n,1) = 2^(n-1) - 1 for n >= 2. (End)

A055810 a(n) = T(n,n-5), array T as in A055807.

Original entry on oeis.org

1, 31, 80, 160, 280, 450, 681, 985, 1375, 1865, 2470, 3206, 4090, 5140, 6375, 7815, 9481, 11395, 13580, 16060, 18860, 22006, 25525, 29445, 33795, 38605, 43906, 49730, 56110, 63080, 70675, 78931, 87885, 97575

Offset: 5

Clark Kimberling, May 28 2000

G. C. Greubel, Table of n, a(n) for n = 5..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A055807, A055809, A055811, A055815, A055816, A055817.

Concatenation([1], List([6..40], n-> (240 -54*n -49*n^2 +6*n^3 +n^4)/24 )); # G. C. Greubel, Jan 23 2020

[1] cat [(240 -54*n -49*n^2 +6*n^3 +n^4)/24: n in [6..40]]; // G. C. Greubel, Jan 23 2020

seq( `if`(n=5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24), n=5..40); # G. C. Greubel, Jan 23 2020

Table[If[n==5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24], {n,5,40}] (* G. C. Greubel, Jan 23 2020 *)

vector(40, n, my(m=n+4); if(m==5, 1, (240 -54*m -49*m^2 +6*m^3 +m^4)/24)) \\ G. C. Greubel, Jan 23 2020

[1]+[(240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n in (6..40)] # G. C. Greubel, Jan 23 2020

G.f.: x^5*(1 +26*x -65*x^2 +60*x^3 -25*x^4 +4*x^5)/(1-x)^5. - Colin Barker, Feb 22 2012
From G. C. Greubel, Jan 23 2020: (Start)
a(n) = (240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n > 5, with a(5) = 1.
E.g.f.: (-1200 -720*x +100*x^3 +25*x^4 -4*x^5 + (1200 -480*x -120*x^2 +60*x^3  +5*x^4)*exp(x))/120. (End)

A055811 a(n) = T(n,n-6), array T as in A055807.

Original entry on oeis.org

1, 63, 192, 432, 832, 1452, 2364, 3653, 5418, 7773, 10848, 14790, 19764, 25954, 33564, 42819, 53966, 67275, 83040, 101580, 123240, 148392, 177436, 210801, 248946, 292361, 341568, 397122, 459612, 529662

Offset: 6

Clark Kimberling, May 28 2000

G. C. Greubel, Table of n, a(n) for n = 6..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A055807, A055809, A055810, A055815, A055816, A055817.

Concatenation([1], List([7..30], n-> n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 )); # G. C. Greubel, Jan 23 2020

[1] cat [n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120: n in [7.30]]; // G. C. Greubel, Jan 23 2020

seq( `if`(n=6, 1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120), n=6..30); # G. C. Greubel, Jan 23 2020

Table[If[n==6,1, n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120], {n,6,30}] (* G. C. Greubel, Jan 23 2020 *)

vector(25, n, my(m=n+5); if(m==6,1, m*(1584 -310*m -85*m^2 +10*m^3 +m^4)/120) ) \\ G. C. Greubel, Jan 23 2020

[1]+[n*(1584 -310*n -85*n^2 +10*n^3 +n^4)/120 for n in (7..30)] # G. C. Greubel, Jan 23 2020

From G. C. Greubel, Jan 23 2020: (Start)
a(n) = n*(1584 - 310*n - 85*n^2 + 10*n^3 + n^4)/120 for n > 6, with a(6) = 1.
G.f.: x^6*(1 + 57*x - 171*x^2 + 205*x^3 - 125*x^4 + 39*x^5 - 5*x^6)/(1-x)^6.
E.g.f.: (-1)*x*(7200 +4320*x +720*x^2 -120*x^3 -54*x^4 +5*x^5 - (7200 -2880*x + 120*x^3 + 6*x^4)*exp(x))/720. (End)

A055815 a(n) = T(2*n+3,n), array T as in A055807.

Original entry on oeis.org

1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Apart from the offset the same as A050149. - R. J. Mathar, Oct 13 2008

Cf. A055807, A055809, A055810, A055811, A055816, A055817.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+3, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+3, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+3, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+3)*hypergeom([-n-2, n], [2], -1) = Sum_{s=1..n+3} binomial(n+3,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

A055816 a(n) = T(2*n+4,n), array T as in A055807.

Original entry on oeis.org

1, 31, 192, 1120, 6400, 36288, 205184, 1159488, 6554880, 37088480, 210075712, 1191254688, 6762782208, 38434677120, 218663320320, 1245254943872, 7098135387648, 40495661150112, 231220652273600, 1321222104326880

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A055807, A055809, A055810, A055811, A055815, A055817.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+4, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+4, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+4, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+4)*hypergeom([-n -3, n], [2], -1) = Sum_{s=1..n+4} binomial(n+4,s)*binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

A055817 a(n) = T(2n+5,n), array T as in A055807.

Original entry on oeis.org

1, 63, 448, 2816, 16896, 99200, 575872, 3322112, 19096064, 109541824, 627653440, 3594256896, 20577979392, 117814911744, 674630384384, 3864033226240, 22138650598400, 126885674577728, 727501822004416, 4172725286118656

Offset: 0

Clark Kimberling, May 28 2000

nonn

G. C. Greubel, Table of n, a(n) for n = 0..250

Cf. A055807, A055809, A055810, A055811, A055815, A055816.

T:= proc(i, j) option remember;
      if j=0 then 1
    elif i=0 then 0
    else add(add(T(h,m), m=0..j), h=0..i-1)
  fi; end:
seq(T(n+5, n), n=0..20); # G. C. Greubel, Jan 23 2020

T[i_, j_]:= T[i, j]= If[j==0, 1, If[i==0, 0, Sum[T[h, m], {h,0,i-1}, {m,0,j}]]]; Table[T[n+5, n], {n,0,20}] (* G. C. Greubel, Jan 23 2020 *)

@CachedFunction
def T(i, j):
    if (j==0): return 1
    elif (i==0): return 0
    else: return sum(sum(T(h,m) for m in (0..j)) for h in (0..i-1))
[T(n+5, n) for n in (0..20)] # G. C. Greubel, Jan 23 2020

a(n) = (n+5)*hypergeom([-n-4, n], [2], -1) = Sum_{s=1..n+5} binomial(n+5,s) * binomial(s+n-2,n-1) for n >= 1. - Petros Hadjicostas, Feb 13 2021

cp's OEIS Frontend

A055203 Number of different relations between n intervals on a line.

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A062109 Expansion of ((1-x)/(1-2*x))^4.

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A055807 Triangle T read by rows: T(i,j) = R(i-j,j), where R(i,0) = 1 for i >= 0, R(0,j) = 0 for j >= 1, and R(i,j) = Sum_{h=0..i-1, k=0..j} R(h,k) for i >= 1 and j >= 1.

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A055810 a(n) = T(n,n-5), array T as in A055807.

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A055811 a(n) = T(n,n-6), array T as in A055807.

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A055815 a(n) = T(2*n+3,n), array T as in A055807.

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