A051865 -id:A051865 - cp's OEIS frontend

A255185 26-gonal numbers: a(n) = n(12n-11).

0, 1, 26, 75, 148, 245, 366, 511, 680, 873, 1090, 1331, 1596, 1885, 2198, 2535, 2896, 3281, 3690, 4123, 4580, 5061, 5566, 6095, 6648, 7225, 7826, 8451, 9100, 9773, 10470, 11191, 11936, 12705, 13498, 14315, 15156, 16021, 16910, 17823, 18760

Offset: 0

Luciano Ancora, Apr 04 2015

See comments in A255184.

Also star 13-gonal number: a(n) = A051865(n) + 13*A000217(n-1).

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (24th row of the table).

Luciano Ancora, Table of n, a(n) for n = 0..1000
Luciano Ancora, Polygonal and Pyramidal numbers, Section 1.
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. similar sequences listed in A255184.

[n*(12*n-11): n in [0..50]]; // G. C. Greubel, Jul 12 2024

Table[n (12 n - 11), {n, 50}]
PolygonalNumber[26,Range[0,50]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,1,26},50] (* Harvey P. Dale, Feb 02 2017 *)

a(n)=n*(12*n-11) \\ Charles R Greathouse IV, Jun 17 2017

[n*(12*n-11) for n in range(51)] # G. C. Greubel, Jul 12 2024

G.f.: x*(1 + 23*x)/(1 - x)^3.
a(n) = A000217(n) + 23*A000217(n-1).
Product_{n>=2} (1 - 1/a(n)) = 12/13. - Amiram Eldar, Jan 22 2021
E.g.f.: exp(x)*(x + 12*x^2). - Nikolaos Pantelidis, Feb 05 2023

A152740 11 times triangular numbers.

Original entry on oeis.org

0, 11, 33, 66, 110, 165, 231, 308, 396, 495, 605, 726, 858, 1001, 1155, 1320, 1496, 1683, 1881, 2090, 2310, 2541, 2783, 3036, 3300, 3575, 3861, 4158, 4466, 4785, 5115, 5456, 5808, 6171, 6545, 6930, 7326, 7733, 8151, 8580, 9020, 9471, 9933, 10406, 10890, 11385, 11891

Offset: 0

Omar E. Pol, Dec 12 2008

Sequence found by reading the line from 0, in the direction 0, 11, ... and the same line from 0, in the direction 0, 33, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Axis perpendicular to A195149 in the same spiral. - Omar E. Pol, Sep 18 2011

Sum of the numbers from 5*n to 6*n. - Wesley Ivan Hurt, Dec 22 2015

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

Cf. A000217, A022268, A022269, A049598, A051865, A069125, A124080, A180223, A195149, A195313, A211013, A218530.

[11*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015

A152740:=n->11*n*(n+1)/2: seq(A152740(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015

Table[11*n*(n - 1)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 11, 33}, 100] (* G. C. Greubel, Dec 22 2015 *)

my(x='x+O('x^100)); concat(0, Vec(11*x/(1-x)^3)) \\ Altug Alkan, Dec 23 2015

a(n) = 11*n*(n+1)/2 = 11*A000217(n).
a(n) = a(n-1) + 11*n with n > 0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
a(n) = A069125(n+1) - 1. - Omar E. Pol, Oct 03 2011
From Philippe Deléham, Mar 27 2013: (Start)
G.f.: 11*x/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=11, a(2)=33.
a(n) = A218530(11*n+10).
a(n) = A211013(n)+n = A022269(n)+5*n = A022268(n)+6*n = A180223(n)+9*n = A051865(n)+10*n. (End)
a(n) = Sum_{i=5*n..6*n} i. - Wesley Ivan Hurt, Dec 22 2015
From Amiram Eldar, Feb 21 2023: (Start)
Sum_{n>=1} 1/a(n) = 2/11.
Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/11.
Product_{n>=1} (1 - 1/a(n)) = -(11/(2*Pi))*cos(sqrt(19/11)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (11/(2*Pi))*cos(sqrt(3/11)*Pi/2). (End)
E.g.f.: 11*exp(x)*x*(2 + x)/2. - Elmo R. Oliveira, Dec 25 2024

A211013 Second 13-gonal numbers: a(n) = n(11n+9)/2.

Original entry on oeis.org

0, 10, 31, 63, 106, 160, 225, 301, 388, 486, 595, 715, 846, 988, 1141, 1305, 1480, 1666, 1863, 2071, 2290, 2520, 2761, 3013, 3276, 3550, 3835, 4131, 4438, 4756, 5085, 5425, 5776, 6138, 6511, 6895, 7290, 7696, 8113, 8541, 8980, 9430, 9891, 10363

Offset: 0

Omar E. Pol, Aug 04 2012

Sequence found by reading the line from 0, in the direction 0, 31... and the line from 10, in the direction 10, 63,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313.

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

Bisection of A195313.
Second k-gonal numbers (k=5..14): A005449, A014105, A147875, A045944, A179986, A033954, A062728, A135705, this sequence, A211014.
Cf. A051865.

List([0..50], n-> n*(11*n+9)/2); # G. C. Greubel, Jul 04 2019

[n*(11*n+9)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019

Table[n*(11*n+9)/2, {n,0,50}] (* G. C. Greubel, Jul 04 2019 *)

a(n)=n*(11*n+9)/2 \\ Charles R Greathouse IV, Jun 17 2017

[n*(11*n+9)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019

G.f.: x*(10+x)/(1-x)^3. - Philippe Deléham, Mar 27 2013
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 0, a(1) = 10, a(2) = 31. - Philippe Deléham, Mar 27 2013
a(n) = A051865(n) + 9n = A180223(n) + 8n = A022268(n) + 5n = A022269(n) + 4n = A152740(n) - n. - Philippe Deléham, Mar 27 2013
a(n) = A218530(11n+9). - Philippe Deléham, Mar 27 2013
E.g.f.: x*(20 + 11*x)*exp(x)/2. - G. C. Greubel, Jul 04 2019

A195528 Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.

Original entry on oeis.org

36, 45, 66, 81, 105, 120, 153, 171, 190, 196, 210, 261, 280, 351, 378, 396, 400, 405, 406, 456, 465, 477, 484, 496, 532, 576, 585, 606, 621, 630, 645, 666, 715, 726, 729, 736, 741, 742, 765, 780, 784, 801, 855, 876, 891, 910, 945, 960, 981, 1015, 1045, 1056

Offset: 1

Ant King, Sep 21 2011

nonn

See A177025 for number of ways a number can be represented as a polygonal number.

			36 is in the sequence because it is a triangular number (A000217), a square number (A000290), a tridecagonal number (A051865), and a 36-gonal number.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A000217, A000290, A051865, A177025, A177029.

data1=Reduce[1/2 n (n(k-2)+4-k)==# && k>=3 && n>0, {k,n}, Integers]&/@Range[1056]; data2=If[Head[#]===And, 1, Length[#]] &/@data1; data3=DeleteCases[Table[If[data2[[k]]==4, k], {k, 1, Length[data2]}], Null]

A195528_list = []
for m in range(1,10**4):
    n, c = 3, 0
    while n*(n+1) <= 2*m:
        if not 2*(n*(n-2) + m) % (n*(n - 1)):
            c += 1
            if c > 3:
                break
        n += 1
    if c == 3:
        A195528_list.append(m) # Chai Wah Wu, Jul 28 2016

A218530 Partial sums of floor(n/11).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 171

Offset: 0

Philippe Deléham, Mar 27 2013

Apart from the initial zeros, the same as A008729.

			As square array:
..0....0....0....0....0....0....0....0....0....0....0
..1....2....3....4....5....6....7....8....9...10...11
.13...15...17...19...21...23...25...27...29...31...33
.36...39...42...45...48...51...54...57...60...63...66
.70...74...78...82...86...90...94...98..102..106..110
115..120..125..130..135..140..145..150..155..160..165
171..177..183..189..195..201..207..213..219..225..231
238..245..252..259..266..273..280..287..294..301..308
316..324..332..340..348..356..364..372..380..388..396
405..414..423..432..441..450..459..468..477..486..495
505..515..525..535..545..555..565..575..585..595..605
...

Cf. similar sequences: A000217, A002820, A130518, A130519, A130520, A174709, A174738, A118729, A218470, A131242.

a(11n)    = A051865(n).
a(11n+1)  = A180223(n).
a(11n+4)  = A022268(n).
a(11n+5)  = A022269(n).
a(11n+6)  = A254963(n)
a(11n+9)  = A211013(n).
a(11n+10) = A152740(n).
G.f.: x^11/((1-x)^2*(1-x^11)).

A264842 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 13-gonal: (11n^2 - 9n)/2.

Original entry on oeis.org

1, 3, 36, 54765, 123152388, 374848814886363636, 85794018663817263665487289502938826, 107072047880615405294526336549204869795454545454545454545454545454545466

Offset: 1

Anders Hellström, Nov 26 2015

			1, 13, 1336, 133654765 are 13-gonal.

Jon E. Schoenfield, Table of n, a(n) for n = 1..11
Wikipedia, Polygonal number

Cf. A051671, A051865 (13-gonal numbers), A061109, A061110, A261696, A264733, A264738, A264776, A264777, A264848, A264849, A264804.

tridecagonal(n)=ispolygonal(n, 13)
first(m)=my(s=""); s="1"; print1(1, ", "); for(i=2, m, n=1; while(!tridecagonal(eval(concat(s, Str(n)))), n++); print1(n, ", "); s=concat(s, Str(n)))

More terms from Jon E. Schoenfield, Nov 27 2015

A317302 Square array T(n,k) = (n - 2)(k - 1)k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 0, 1, 1, -3, 0, 1, 2, 0, -8, 0, 1, 3, 3, -2, -15, 0, 1, 4, 6, 4, -5, -24, 0, 1, 5, 9, 10, 5, -9, -35, 0, 1, 6, 12, 16, 15, 6, -14, -48, 0, 1, 7, 15, 22, 25, 21, 7, -20, -63, 0, 1, 8, 18, 28, 35, 36, 28, 8, -27, -80, 0, 1, 9, 21, 34, 45, 51, 49, 36, 9, -35, -99, 0, 1, 10, 24, 40, 55, 66

Offset: 0

Omar E. Pol, Aug 09 2018

Note that the formula gives several kinds of numbers, for example:
Row 0 gives 0 together with A258837.
Row 1 gives 0 together with A080956.
Row 2 gives A001477, the nonnegative numbers.
For n >= 3, row n gives the n-gonal numbers (see Crossrefs section).

			Array begins:
------------------------------------------------------------------------
n\k  Numbers       Seq. No.   0   1   2   3   4    5    6    7    8
------------------------------------------------------------------------
0    ............ (A258837):  0,  1,  0, -3, -8, -15, -24, -35, -48, ...
1    ............ (A080956):  0,  1,  1,  0, -2,  -5,  -9, -14, -20, ...
2    Nonnegatives  A001477:   0,  1,  2,  3,  4,   5,   6,   7,   8, ...
3    Triangulars   A000217:   0,  1,  3,  6, 10,  15,  21,  28,  36, ...
4    Squares       A000290:   0,  1,  4,  9, 16,  25,  36,  49,  64, ...
5    Pentagonals   A000326:   0,  1,  5, 12, 22,  35,  51,  70,  92, ...
6    Hexagonals    A000384:   0,  1,  6, 15, 28,  45,  66,  91, 120, ...
7    Heptagonals   A000566:   0,  1,  7, 18, 34,  55,  81, 112, 148, ...
8    Octagonals    A000567:   0,  1,  8, 21, 40,  65,  96, 133, 176, ...
9    9-gonals      A001106:   0,  1,  9, 24, 46,  75, 111, 154, 204, ...
10   10-gonals     A001107:   0,  1, 10, 27, 52,  85, 126, 175, 232, ...
11   11-gonals     A051682:   0,  1, 11, 30, 58,  95, 141, 196, 260, ...
12   12-gonals     A051624:   0,  1, 12, 33, 64, 105, 156, 217, 288, ...
13   13-gonals     A051865:   0,  1, 13, 36, 70, 115, 171, 238, 316, ...
14   14-gonals     A051866:   0,  1, 14, 39, 76, 125, 186, 259, 344, ...
15   15-gonals     A051867:   0,  1, 15, 42, 82, 135, 201, 280, 372, ...
...

Omar E. Pol, Polygonal numbers.
The OEIS, Polygonal numbers.
University of Surrey, Dept. of Mathematics, Polygonal Numbers - or Numbers as Shapes.
Eric Weisstein's World of Mathematics, Figurate Number.
Eric Weisstein's World of Mathematics, Polygonal Number.
Wikipedia, Polygonal number.
Index to sequences related to polygonal numbers

Column 0 gives A000004.
Column 1 gives A000012.
Column 2 gives A001477, which coincides with the row numbers.
Main diagonal gives A060354.
Row 0 gives 0 together with A258837.
Row 1 gives 0 together with A080956.
Row 2 gives A001477, the same as column 2.
For n >= 3, row n gives the n-gonal numbers: A000217 (n=3), A000290 (n=4), A000326 (n=5), A000384 (n=6), A000566 (n=7), A000567 (n=8), A001106 (n=9), A001107 (n=10), A051682 (n=11), A051624 (n=12), A051865 (n=13), A051866 (n=14), A051867 (n=15), A051868 (n=16), A051869 (n=17), A051870 (n=18), A051871 (n=19), A051872 (n=20), A051873 (n=21), A051874 (n=22), A051875 (n=23), A051876 (n=24), A255184 (n=25), A255185 (n=26), A255186 (n=27), A161935 (n=28), A255187 (n=29), A254474 (n=30).
Cf. A139600, A139601.
Cf. A303301 (similar table but with generalized polygonal numbers).

T(n,k) = A139600(n-2,k) if n >= 2.

T(n,k) = A139601(n-3,k) if n >= 3.

A008729 Molien series for 3-dimensional group [2, n] = *22n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219

Offset: 0

N. J. A. Sloane

			..1....2....3....4....5....6....7....8....9...10...11
.13...15...17...19...21...23...25...27...29...31...33
.36...39...42...45...48...51...54...57...60...63...66
.70...74...78...82...86...90...94...98..102..106..110
115..120..125..130..135..140..145..150..155..160..165
171..177..183..189..195..201..207..213..219..225..231
238..245..252..259..266..273..280..287..294..301..308
316..324..332..340..348..356..364..372..380..388..396
405..414..423..432..441..450..459..468..477..486..495
505..515..525..535..545..555..565..575..585..595..605
...
The first six columns are A051865, A180223, A022268, A022269, A211013, A152740.
- _Philippe Deléham_, Apr 03 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 194
Index entries for Molien series
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,1,-2,1).

Cf. A001840, A001972, A008724-A008728, A008732, A218530.

a:=[1,2,3,4,5,6,7,8,9,10,11,13,15];; for n in [14..70] do a[n]:=2*a[n-1]-a[n-2]+a[n-11]-2*a[n-12]+a[n-13]; od; a; # G. C. Greubel, Jul 30 2019

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^11)) )); // G. C. Greubel, Jul 30 2019

g:= 1/((1-x)^2*(1-x^11)); gser:= series(g, x=0,72); seq(coeff(gser, x, n), n=0..70); # modified by G. C. Greubel, Jul 30 2019

CoefficientList[Series[1/((1-x)^2*(1-x^11)), {x,0,70}], x] (* Vincenzo Librandi, Jun 11 2013 *)

my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^11))) \\ G. C. Greubel, Jul 30 2019

(1/((1-x)^2*(1-x^11))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

From Mitch Harris, Sep 08 2008: (Start)
a(n) = Sum_{j=0..n+11} floor(j/11).
a(n-11) = (1/2)*floor(n/11)*(2*n - 9 - 11*floor(n/11)). (End)
a(n) = A218530(n+11). - Philippe Deléham, Apr 03 2013
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 2*a(n-1) - a(n-2) + a(n-11) - 2*a(n-12) + a(n-13) for n > 12.
G.f.: 1/(1 - 2*x + x^2 - x^11 + 2*x^12 - x^13) = 1/((1-x)^3 *(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)). (End)

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

A055268 a(n) = (11n + 4)C(n+3, 3)/4.

Original entry on oeis.org

1, 15, 65, 185, 420, 826, 1470, 2430, 3795, 5665, 8151, 11375, 15470, 20580, 26860, 34476, 43605, 54435, 67165, 82005, 99176, 118910, 141450, 167050, 195975, 228501, 264915, 305515, 350610, 400520, 455576, 516120, 582505, 655095, 734265

Offset: 0

Barry E. Williams, May 10 2000

a(n) is the number of compositions of n when there are 9 types of each natural number. - Milan Janjic, Aug 13 2010

Convolution of A000027 with A051865 (excluding 0). - Bruno Berselli, Dec 07 2012

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.

G. C. Greubel, Table of n, a(n) for n = 0..1000
I. Adler, Three Diophantine equations - Part II, Fib. Quart., 7 (1969), pp. 181-193.
E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.
Index to sequences related to pyramidal numbers
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Partial sums of A050441.
Cf. A000292, A051865.
Cf. A220212 for a list of sequences produced by the convolution of the natural numbers with the k-gonal numbers.

List([0..30], n-> (11*n+4)*Binomial(n+3,3)/4 ); # G. C. Greubel, Jan 17 2020

/* A000027 convolved with A051865 (excluding 0): */ A051865:=func; [&+[(n-i+1)*A051865(i): i in [1..n]]: n in [1..35]]; // Bruno Berselli, Dec 07 2012

seq( (11*n+4)*binomial(n+3,3)/4, n=0..30); # G. C. Greubel, Jan 17 2020

Table[11*Binomial[n+4,4] -10*Binomial[n+3,3], {n,0,30}] (* G. C. Greubel, Jan 17 2020 *)

a(n) = (11*n+4)*binomial(n+3, 3)/4; \\ Michel Marcus, Sep 07 2017

A055268_list, m = [], [11, 1, 1, 1, 1]
for _ in range(10**2):
    A055268_list.append(m[-1])
    for i in range(4):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

[(11*n+4)*binomial(n+3,3)/4 for n in (0..30)] # G. C. Greubel, Jan 17 2020

G.f.: (1 + 10*x)/(1-x)^5. - R. J. Mathar, Oct 26 2011
From G. C. Greubel, Jan 17 2020:(Start)
a(n) = 11*binomial(n+4,4) - 10*binomial(n+3,3).
E.g.f.: (24 + 336*x + 432*x^2 + 136*x^3 + 11*x^4)*exp(x)/24. (End)

A226491 a(n) = n(21n-17)/2.

Original entry on oeis.org

0, 2, 25, 69, 134, 220, 327, 455, 604, 774, 965, 1177, 1410, 1664, 1939, 2235, 2552, 2890, 3249, 3629, 4030, 4452, 4895, 5359, 5844, 6350, 6877, 7425, 7994, 8584, 9195, 9827, 10480, 11154, 11849, 12565, 13302, 14060, 14839, 15639, 16460, 17302, 18165, 19049, 19954

Offset: 0

Bruno Berselli, Jun 09 2013

Sum of n-th dodecagonal number and n-th tridecagonal number.

Sum of reciprocals of a(n), for n > 0: 0.58517199913243139233033474262449...

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A051624, A051865, A064762.

Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=21: see list in A226488.

Magma
```
[n*(21*n-17)/2: n in [0..50]];
```

I:=[0,2,25]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013

Table[n (21 n - 17)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 19 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{3,-3,1},{0,2,25},50] (* Harvey P. Dale, Feb 01 2023 *)

a(n)=n*(21*n-17)/2 \\ Charles R Greathouse IV, Jun 17 2017

G.f.: x*(2+19*x)/(1-x)^3.
a(n) + a(-n) = A064762(n).
From Elmo R. Oliveira, Jan 12 2025: (Start)
E.g.f.: exp(x)*x*(4 + 21*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

cp's OEIS Frontend

A255185 26-gonal numbers: a(n) = n*(12*n-11).

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A152740 11 times triangular numbers.

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A211013 Second 13-gonal numbers: a(n) = n*(11*n+9)/2.

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A195528 Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.

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A218530 Partial sums of floor(n/11).

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A264842 a(n) is least number > 0 such that the concatenation of a(1) ... a(n) is 13-gonal: (11n^2 - 9n)/2.

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A317302 Square array T(n,k) = (n - 2)*(k - 1)*k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

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A255185 26-gonal numbers: a(n) = n(12n-11).

A211013 Second 13-gonal numbers: a(n) = n(11n+9)/2.

A317302 Square array T(n,k) = (n - 2)(k - 1)k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

A055268 a(n) = (11n + 4)C(n+3, 3)/4.

A226491 a(n) = n(21n-17)/2.