A006322 -id:A006322 - cp's OEIS frontend

A236770 a(n) = n(n + 1)(3n^2 + 3n - 2)/8.

0, 1, 12, 51, 145, 330, 651, 1162, 1926, 3015, 4510, 6501, 9087, 12376, 16485, 21540, 27676, 35037, 43776, 54055, 66045, 79926, 95887, 114126, 134850, 158275, 184626, 214137, 247051, 283620, 324105, 368776, 417912, 471801, 530740, 595035, 665001, 740962

Offset: 0

Bruno Berselli, Jan 31 2014

After 0, first trisection of A011779 and right border of A177708.

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Partial sums of A004188.
Cf. A000217, A000332, A011779, A177708.
Cf. similar sequences on the polygonal numbers: A002817(n) = A000217(A000217(n)); A000537(n) = A000290(A000217(n)); A037270(n) = A000217(A000290(n)); A062392(n) = A000384(A000217(n)).
Cf. sequences of the form A000217(m)+k*A000332(m+2): A062392 (k=12); A264854 (k=11); A264853 (k=10); this sequence (k=9); A006324 (k=8); A006323 (k=7); A000537 (k=6); A006322 (k=5); A006325 (k=4), A002817 (k=3), A006007 (k=2), A006522 (k=1).
Cf. A232713, A260810.

[n*(n+1)*(3*n^2+3*n-2)/8: n in [0..40]];

Table[n (n + 1) (3 n^2 + 3 n - 2)/8, {n, 0, 40}]
LinearRecurrence[{5,-10,10,-5,1},{0,1,12,51,145},40] (* Harvey P. Dale, Aug 22 2016 *)

for(n=0, 40, print1(n*(n+1)*(3*n^2+3*n-2)/8", "));

G.f.: x*(1 + 7*x + x^2)/(1 - x)^5.
a(n) = a(-n-1) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = A000326(A000217(n)).
a(n) = A000217(n) + 9*A000332(n+2).
Sum_{n>=1} 1/a(n) = 2 + 4*sqrt(3/11)*Pi*tan(sqrt(11/3)*Pi/2) = 1.11700627139319... . - Vaclav Kotesovec, Apr 27 2016

A085461 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1 <= v5, v2 <= v5, v2 <= v4 and v3 <= v4.

Original entry on oeis.org

1, 13, 70, 246, 671, 1547, 3164, 5916, 10317, 17017, 26818, 40690, 59787, 85463, 119288, 163064, 218841, 288933, 375934, 482734, 612535, 768867, 955604, 1176980, 1437605, 1742481, 2097018, 2507050, 2978851, 3519151, 4135152, 4834544

Offset: 1

Goran Kilibarda, Vladeta Jovovic, Jul 01 2003

Number of monotone n-weightings of a certain connected bipartite digraph. A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,...,n-1} such that w(v1) <= w(v2) for every arc (v1,v2) from E.
Kekulé numbers for certain benzenoids. - Emeric Deutsch, Nov 18 2005
Can be constructed by taking the product of the three members of a Pythagorean triples and dividing by 60. Formula: n*(n^2-1)*(n^2+1)/240 where n runs through the odd numbers >= 3. - Pierre Gayet, Apr 04 2009
Number of composable morphisms in a height-n tower of retractions. A retraction between objects X and Y is a pair of maps s:X->Y and r:Y->X such that r(s(x))=x for all x in X. Given objects X_0,X_1,X_2,...,X_n, we can ask for retractions s_i:X_i->X_{i+1},r_i:X_{i+1}->X_i, for each 0 <= i < n. The total number of morphisms in that category is 0^2 + 1^2 + 2^2 + ... + n^2 (cf. A000330). The total number of composable pairs of morphisms in that category is the sequence given here. - David Spivak, Feb 26 2014

S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 168).

G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Daeseok Lee and H.-K. Ju, An Extension of Hibi's palindromic theorem, arXiv preprint arXiv:1503.05658 [math.CO], 2015.
R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]
See p. 31
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A006322, A006325, A079547, A085462, A085463, A085464, A085465.

Rest[CoefficientList[Series[x*(1 + x)*(1 + 6*x + x^2)/(1 - x)^6, {x, 0, 50}], x]] (* G. C. Greubel, Oct 06 2017 *)

x='x+O('x^50); Vec(x*(1+x)*(1+6*x+x^2)/(1-x)^6) \\ G. C. Greubel, Oct 06 2017

a(n) = n + 11*binomial(n, 2) + 34*binomial(n, 3) + 40*binomial(n, 4) + 16*binomial(n, 5) = 1/30*n*(n+1)*(2*n+1)*(2*n^2 + 2*n + 1).
From Bruno Berselli, Dec 27 2010: (Start)
G.f.: x*(1+x)*(1+6*x+x^2)/(1-x)^6.
a(n) = ( n*A110450(n) - Sum_{i=0..n-1} A110450(i) )/3. (End)

A085465 Number of monotone n-weightings of complete bipartite digraph K(3,3).

Original entry on oeis.org

1, 15, 102, 442, 1443, 3885, 9100, 19188, 37269, 67771, 116754, 192270, 304759, 467481, 696984, 1013608, 1442025, 2011815, 2758078, 3722082, 4951947, 6503365, 8440356, 10836060, 13773565, 17346771, 21661290, 26835382, 33000927, 40304433

Offset: 1

Goran Kilibarda, Vladeta Jovovic, Jul 01 2003

A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.

a(n) = number of proper mergings of a 3-antichain and an (n-1)-chain. - Henri Mühle, Aug 17 2012

G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
H. Mühle, Counting Proper Mergings of Chains and Antichains, arXiv:1206.3922 [math.CO], 2012.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A006003, A006322, A006325, A079547, A085461-A085465.

[1/20*n*(n+1)*(n^2+1)*(n^2+2*n+2): n in [1..40]]; // Vincenzo Librandi, Oct 06 2017

Rest[CoefficientList[Series[x*(1 + 4*x + x^2)^2/(1 - x)^7, {x, 0, 50}], x]] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 15, 102, 442, 1443, 3885, 9100}, 40] (* Vincenzo Librandi, Oct 06 2017 *)

x='x+O('x^50); Vec(x*(1+4*x+x^2)^2/(1-x)^7) \\ G. C. Greubel, Oct 06 2017

a(n) = n + 13*binomial(n, 2) + 60*binomial(n, 3) + 120*binomial(n, 4) + 108*binomial(n, 5) + 36*binomial(n, 6) = 1/20*n*(n+1)*(n^2+1)*(n^2+2*n+2) = Sum_{i=1..n} ((n+1-i)^3-(n-i)^3)*i^3. More generally, number of monotone n-weightings of complete bipartite digraph K(s, t) is Sum_{i=1..n} ((n+1-i)^s-(n-i)^s)*i^t = Sum_{i=1..n} ((n+1-i)^t-(n-i)^t)*i^s.
G.f.: x*(1+4*x+x^2)^2/(1-x)^7. - Colin Barker, Apr 01 2012
a(n) = A006003(n)*A006003(n+1)/5 for n>0. - Bruno Berselli, Jun 26 2018

A085462 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4 and v3<=v4.

Original entry on oeis.org

1, 14, 77, 273, 748, 1729, 3542, 6630, 11571, 19096, 30107, 45695, 67158, 96019, 134044, 183260, 245973, 324786, 422617, 542717, 688688, 864501, 1074514, 1323490, 1616615, 1959516, 2358279, 2819467, 3350138, 3957863, 4650744

Offset: 1

Goran Kilibarda and Vladeta Jovovic, Jul 01 2003

Number of monotone n-weightings of a certain connected bipartite digraph. A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.

Dimensions of certain Lie algebra (see Landsberg-Manivel reference for precise definition). - N. J. A. Sloane, Oct 15 2007

G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=-2/3]
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A006322, A006325, A079547, A085461, A085463, A085464, A085465.

[n*(n+1)*(2*n+1)*(3*n+1)*(3*n+2)/120: n in [0..50]]; // G. C. Greubel, Oct 07 2017

Rest[CoefficientList[Series[x*(1 + x)*(1 + 7*x + x^2)/(1 - x)^6, {x, 0, 50}], x]] (* or *) Table[n*(n+1)*(2*n+1)*(3*n+1)*(3*n+2)/120, {n,0,50}] (* G. C. Greubel, Oct 07 2017 *)

x='x+O('x^50); Vec(x*(1+x)*(1+7*x+x^2)/(1-x)^6) \\ G. C. Greubel, Oct 07 2017

a(n) = n + 12*binomial(n, 2) + 38*binomial(n, 3) + 45*binomial(n, 4) + 18*binomial(n, 5).
a(n) = n*(n+1)*(2*n+1)*(3*n+1)*(3*n+2)/120.
G.f.: x*(1+x)*(1+7*x+x^2)/(1-x)^6. - Colin Barker, Apr 01 2012
a(n) = sum(i=1..n, sum(j=1..n, i^2 * Min(i,j))). - Enrique Pérez Herrero, Jan 30 2013

A085463 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4, v2<=v5 and v3<=v4.

Original entry on oeis.org

1, 12, 63, 219, 594, 1365, 2786, 5202, 9063, 14938, 23529, 35685, 52416, 74907, 104532, 142868, 191709, 253080, 329251, 422751, 536382, 673233, 836694, 1030470, 1258595, 1525446, 1835757, 2194633, 2607564, 3080439, 3619560, 4231656

Offset: 1

Goran Kilibarda, Vladeta Jovovic, Jul 01 2003

Number of monotone n-weightings of a certain connected bipartite digraph. A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A006322, A006325, A079547, A085461-A085465.

[n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120: n in [1..25]]; // G. C. Greubel, Oct 07 2017

Table[n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120, {n,1,25}] (* G. C. Greubel, Oct 07 2017 *)

for(n=1,25, print1(n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120, ", ")) \\ G. C. Greubel, Oct 07 2017

a(n) = n + 10*binomial(n, 2) + 30*binomial(n, 3) + 35*binomial(n, 4) + 14*binomial(n, 5).
a(n) = n*(n+1)*(2*n+1)*(7*n^2 + 7*n + 6)/120.
G.f.: x*(1+6*x+6*x^2+x^3)/(1-x)^6. - Colin Barker, Apr 01 2012

A085464 Number of monotone n-weightings of complete bipartite digraph K(4,2).

Original entry on oeis.org

1, 19, 134, 586, 1919, 5173, 12124, 25572, 49677, 90343, 155650, 256334, 406315, 623273, 929272, 1351432, 1922649, 2682363, 3677374, 4962706, 6602519, 8671069, 11253716, 14447980, 18364645, 23128911, 28881594, 35780374, 44001091

Offset: 1

Goran Kilibarda and Vladeta Jovovic, Jul 01 2003

A monotone n-(vertex) weighting of a digraph D=(V,E) is a function w: V -> {0,1,..,n-1} such that w(v1)<=w(v2) for every arc (v1,v2) from E.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.

Cf. A006322, A006325, A079547, A085461, A085462, A085463, A085465.

[(1/30)*n*(n+1)*(2*n^4+4*n^3+6*n^2+4*n-1): n in [1..25]]; // G. C. Greubel, Oct 07 2017

Table[(1/30)*n*(n+1)*(2*n^4+4*n^3+6*n^2+4*n-1), {n,1,50}] (* G. C. Greubel, Oct 07 2017 *)

a(n)=n*(n+1)*(2*n^4+4*n^3+6*n^2+4*n-1)/30 \\ Charles R Greathouse IV, Jan 16 2013

a(n) = n + 17*binomial(n, 2) + 80*binomial(n, 3) + 160*binomial(n, 4) + 144*binomial(n, 5) + 48*binomial(n, 6).
a(n) = (1/30)*n*(n+1)*(2*n^4+4*n^3+6*n^2+4*n-1).
a(n) = Sum_{i=1..n} ((n+1-i)^4-(n-i)^4)*i^2.
a(n) = Sum_{i=1..n} ((n+1-i)^2-(n-i)^2)*i^4.
More generally, number of monotone n-weightings of complete bipartite digraph K(s, t) is Sum_{i=1..n} ((n+1-i)^s-(n-i)^s)*i^t = Sum_{i=1..n} ((n+1-i)^t-(n-i)^t)*i^s.
G.f.: x*(1+x)^2*(1+10*x+x^2)/(1-x)^7. - Colin Barker, Apr 01 2012
a(n) = sum(i=1..n, sum (j=1..n, min(i,j)^4)). - Enrique Pérez Herrero, Jan 16 2013

A264854 a(n) = n(n + 1)(11n^2 + 11n - 10)/24.

Original entry on oeis.org

0, 1, 14, 61, 175, 400, 791, 1414, 2346, 3675, 5500, 7931, 11089, 15106, 20125, 26300, 33796, 42789, 53466, 66025, 80675, 97636, 117139, 139426, 164750, 193375, 225576, 261639, 301861, 346550, 396025, 450616, 510664, 576521, 648550, 727125, 812631, 905464, 1006031

Offset: 0

Ilya Gutkovskiy, Nov 26 2015

Partial sums of centered 11-gonal (or hendecagonal) pyramidal numbers.

OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A004467.

Cf. similar sequences provided by the partial sums of centered k-gonal pyramidal numbers: A006522 (k=1), A006007 (k=2), A002817 (k=3), A006325 (k=4), A006322 (k=5), A000537 (k=6), A006323 (k=7), A006324 (k=8), A236770 (k=9), A264853 (k=10), this sequence (k=11), A062392 (k=12), A264888 (k=13).

[n*(n+1)*(11*n^2+11*n-10)/24: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015

Table[n (n + 1) (11 n^2 + 11 n - 10)/24, {n, 0, 50}]

a(n)=n*(n+1)*(11*n^2+11*n-10)/24 \\ Charles R Greathouse IV, Jul 26 2016

G.f.: x*(1 + 9*x + x^2)/(1 - x)^5.
a(n) = Sum_{k = 0..n} A004467(k).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015

A362863 Centered hecatonicosachoral numbers.

Original entry on oeis.org

1, 1441, 11521, 44641, 122401, 273601, 534241, 947521, 1563841, 2440801, 3643201, 5243041, 7319521, 9959041, 13255201, 17308801, 22227841, 28127521, 35130241, 43365601, 52970401, 64088641, 76871521, 91477441, 108072001, 126828001, 147925441, 171551521, 197900641

Offset: 1

Léo Cymrot Cymbalista, May 06 2023

A hecatonicosachoral number is a centered figurate number that represents a hecatonicosachoron, which is a four-dimensional regular polytope composed of 120 cells.

One of the 6 centered regular polichoral (centered pentachoral, centered hexadecachoral, centered octachoral, centered icositetrachoral, centered hexacosichoral and centered hecatonicosachoral) numbers.

Eric Weisstein's World of Mathematics, Figurate Number.
Wikipedia, 120-cell.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A005891 (2D), A005904 (3D), A006322, A151989.

Table[300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1, {n, 1, 100}]

a(n) = 300*n^4 - 600*n^3 + 420*n^2 - 120*n + 1.
a(n) = 1440*A006322(n-1) + 1 for n > 1.
a(n) = 288*(A151989(n-1)-1)/25 + 1.
G.f.: x*(1 + 1436*x + 4326*x^2 + 1436*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, May 12 2023

A071910 a(n) = t(n)t(n+1)t(n+2), where t() are the triangular numbers.

Original entry on oeis.org

0, 18, 180, 900, 3150, 8820, 21168, 45360, 89100, 163350, 283140, 468468, 745290, 1146600, 1713600, 2496960, 3558168, 4970970, 6822900, 9216900, 12273030, 16130268, 20948400, 26910000, 34222500, 43120350, 53867268, 66758580, 82123650, 100328400, 121777920

Offset: 0

N. J. A. Sloane, Jun 13 2002

nonn

a(n) is also the number of three-dimensional cage assemblies such that the assembly is not a cube. See also A052149 for the two-dimensional version and to A059827 for the non-exclusive version. - Alejandro Rodriguez, Oct 20 2020

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A006542, (first differences of a(n) /18) A006414, (second differences of a(n) /18) A006322, (third differences of a(n) /18) A004068, (fourth differences of a(n) /18) A005891, (fifth differences of a(n) /18) A008706.

Join[{0},Times@@@Partition[Accumulate[Range[40]],3,1]] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,18,180,900,3150,8820,21168},40] (* Harvey P. Dale, Aug 08 2025 *)

t(n) = n*(n+1)/2;
a(n) = t(n)*t(n+1)*t(n+2); \\ Michel Marcus, Oct 21 2015

a(n) = 18*A006542(n+3). - Vladeta Jovovic, Jun 14 2002
G.f.: 18*x*(1+3*x+x^2)/(1-x)^7. - Vladeta Jovovic, Jun 14 2002
a(n) = ((n+1)*(n+2))^3/8 - Sum_{i=1..n+1} i^3. - Jon Perry, Feb 13 2004
a(n) = C(2+n, n)*C(3+n, 1+n)*C(4+n, 2+n). - Zerinvary Lajos, Jul 29 2005
a(n) = A059827(n+1) - A000537(n+1). - Michel Marcus, Oct 21 2015

A373424 Array read by ascending antidiagonals: T(n, k) = [x^k] cf(n) where cf(n) is the continued fraction (-1)^n/(~x - 1/(~x - ... 1/(~x - 1)))...) and where '~' is '-' if n is even, and '+' if n is odd, and x appears n times in the expression.

Original entry on oeis.org

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 6, 5, 1, 0, 1, 5, 10, 14, 8, 1, 0, 1, 6, 15, 30, 31, 13, 1, 0, 1, 7, 21, 55, 85, 70, 21, 1, 0, 1, 8, 28, 91, 190, 246, 157, 34, 1, 0, 1, 9, 36, 140, 371, 671, 707, 353, 55, 1, 0, 1, 10, 45, 204, 658, 1547, 2353, 2037, 793, 89, 1, 0

Offset: 0

Peter Luschny, Jun 09 2024

A variant of both A050446 and A050447 which are the main entries. Differs in indexing and adds a first row to the array resp. a diagonal to the triangle.

			Generating functions of the rows:
   gf0 =  1;
   gf1 = -1/( x-1);
   gf2 =  1/(-x-1/(-x-1));
   gf3 = -1/( x-1/( x-1/( x-1)));
   gf4 =  1/(-x-1/(-x-1/(-x-1/(-x-1))));
   gf5 = -1/( x-1/( x-1/( x-1/( x-1/( x-1)))));
   gf6 =  1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1))))));
   ...
Array A(n, k) starts:
  [0] 1, 0,  0,  0,   0,    0,    0,     0,      0,      0, ...  A000007
  [1] 1, 1,  1,  1,   1,    1,    1,     1,      1,      1, ...  A000012
  [2] 1, 2,  3,  5,   8,   13,   21,    34,     55,     89, ...  A000045
  [3] 1, 3,  6, 14,  31,   70,  157,   353,    793,   1782, ...  A006356
  [4] 1, 4, 10, 30,  85,  246,  707,  2037,   5864,  16886, ...  A006357
  [5] 1, 5, 15, 55, 190,  671, 2353,  8272,  29056, 102091, ...  A006358
  [6] 1, 6, 21, 91, 371, 1547, 6405, 26585, 110254, 457379, ...  A006359
   A000027,A000330,   A085461,     A244881, ...
       A000217, A006322,    A108675, ...
.
Triangle T(n, k) = A(n - k, k) starts:
  [0] 1;
  [1] 1,  0;
  [2] 1,  1,  0;
  [3] 1,  2,  1,  0;
  [4] 1,  3,  3,  1,  0;
  [5] 1,  4,  6,  5,  1,  0;
  [6] 1,  5, 10, 14,  8,  1, 0;

T. Kyle Petersen and Yan Zhuang, Zig-zag Eulerian polynomials, arXiv:2403.07181 [math.CO], 2024. (Table 3)

Cf. A050446, A050447, A276313 (main diagonal), A373353 (row sums of triangle).

Cf. A373423.

row := proc(n, len) local x, a, j, ser; if irem(n, 2) = 1 then
a :=  x - 1; for j from 1 to n do a :=  x - 1 / a od: a :=  a - x; else
a := -x - 1; for j from 1 to n do a := -x - 1 / a od: a := -a - x;
fi; ser := series(a, x, len + 2); seq(coeff(ser, x, j), j = 0..len) end:
A := (n, k) -> row(n, 12)[k+1]:      # array form
T := (n, k) -> row(n - k, k+1)[k+1]: # triangular form

def Arow(n, len):
    R. = PowerSeriesRing(ZZ, len)
    if n == 0: return [1] + [0]*(len - 1)
    x = -x if n % 2 else x
    a = x + 1
    for _ in range(n):
        a = x - 1 / a
    a = x - a if n % 2 else a - x
    return a.list()
for n in range(7): print(Arow(n, 10))

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A236770 a(n) = n*(n + 1)*(3*n^2 + 3*n - 2)/8.

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A085461 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1 <= v5, v2 <= v5, v2 <= v4 and v3 <= v4.

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A085465 Number of monotone n-weightings of complete bipartite digraph K(3,3).

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A085462 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4 and v3<=v4.

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A085463 Number of 5-tuples (v1,v2,v3,v4,v5) of nonnegative integers less than n such that v1<=v4, v1<=v5, v2<=v4, v2<=v5 and v3<=v4.

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A085464 Number of monotone n-weightings of complete bipartite digraph K(4,2).

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A264854 a(n) = n*(n + 1)*(11*n^2 + 11*n - 10)/24.

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A236770 a(n) = n(n + 1)(3n^2 + 3n - 2)/8.

A264854 a(n) = n(n + 1)(11n^2 + 11n - 10)/24.

A071910 a(n) = t(n)t(n+1)t(n+2), where t() are the triangular numbers.