A017281 -id:A017281 - cp's OEIS frontend

A017282 a(n) = (10*n + 1)^2.

1, 121, 441, 961, 1681, 2601, 3721, 5041, 6561, 8281, 10201, 12321, 14641, 17161, 19881, 22801, 25921, 29241, 32761, 36481, 40401, 44521, 48841, 53361, 58081, 63001, 68121, 73441, 78961, 84681, 90601, 96721, 103041, 109561, 116281, 123201

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m=3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), A017174 (m=9), this sequence (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Cf. A017281.

[(10*n+1)^2: n in [0..35]]; // Vincenzo Librandi, Jul 30 2011

(* Programs from Michael De Vlieger, Mar 30 2017 *)
Table[(10 n+1)^2, {n, 0, 35}]
FoldList[#1 + 200 #2 - 80 &, 1, Range@ 35]
CoefficientList[Series[(1+118x+81x^2)/(1-x)^3, {x,0,35}], x] (* End *)
LinearRecurrence[{3,-3,1},{1,121,441},40] (* Harvey P. Dale, Sep 21 2017 *)

for(n=0, 35, print1((10*n+1)^2", ")); \\ Bruno Berselli, Jul 30 2011

[(10*n+1)^2 for n in range(51)] # G. C. Greubel, Dec 24 2022

G.f.: (1+118*x+81*x^2)/(1-x)^3. - Bruno Berselli, Jul 30 2011
a(n) = a(n-1) + 40*(5*n-2), n > 0; a(0)=1. - Miquel Cerda, Oct 30 2016
a(n) = A017281(n)^2. - Michel Marcus, Oct 30 2016
E.g.f.: (1 +120*x +100*x^2)*exp(x). - G. C. Greubel, Dec 24 2022

More terms from Bruno Berselli, Jul 30 2011

A350000 Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of cells in a regular n-gon after k generations of mitosis.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 4, 11, 1, 1, 4, 21, 24, 1, 1, 4, 31, 42, 50, 1, 1, 4, 41, 42, 190, 80, 1, 1, 4, 51, 42, 400, 152, 154, 1, 1, 4, 61, 42, 680, 152, 802, 220, 1, 1, 4, 71, 42, 1030, 152, 1792, 590, 375, 1, 1, 4, 81, 42, 1450, 152, 2962, 690, 2091, 444, 1

Offset: 3

Scott R. Shannon and N. J. A. Sloane, Dec 06 2021

We use "cell" in the sense of planar graph theory, meaning a "region" or two-dimensional face.
We start at generation 0 with a regular n-gon with a single cell.
At each stage the mitosis process splits each cell into smaller cells by drawing chords between every pair of points on the boundary of that cell.
For the first few generations of mitosis of a triangle, square, pentagon, and hexagon, see the sketch in one of the links below.
The process of going from generation 0 to generation 1 was analyzed by Poonen and Rubinstein (1998) - see A007678 and A331450.
It is worth enlarging the illustrations in order to see the detailed structure and the cell counts in the upper left corner. The illustrations for the mitosis of a 7-gon can be seen in A349808 and are not repeated here.
Conjecture 1: For a fixed value of n, there are integers r and s, which are small compared to n, such that T(n,k) is a polynomial in k of degree r for all k >= s.
For example, T(11,k) = 220*k^2 + 1452*k - 1693 for k >= 2. See the Formulas section below for further examples.
Note that if n is odd, all generations of mitosis of a regular n-gon contain a (smaller) regular n-gon at their center.
Conjecture 2: Apart from the central n-gon when n is odd, any cell will eventually split into a mixture of triangles and pentagons.
If we think of triangles and pentagons are harmless cells, and all other cells as dangerous, the conjecture states that (with the exception of the central odd cells), all cells eventually become harmless.

			The table begins:
.
      |               Number of polygons after k generations
  n\k | 0,    1,     2,     3,      4,      5,      6,      7,      8,      9, ...
----------------------------------------------------------------------------------
   3  | 1,    1,     1,     1,      1,      1,      1,      1,      1,      1, ...
   4  | 1,    4,     4,     4,      4,      4,      4,      4,      4,      4, ...
   5  | 1,   11,    21,    31,     41,     51,     61,     71,     81,     91, ...
   6  | 1,   24,    42,    42,     42,     42,     42,     42,     42,     42, ...
   7  | 1,   50,   190,   400,    680,   1030,   1450,   1940,   2500,   3130, ...
   8  | 1,   80,   152,   152,    152,    152,    152,    152,    152,    152, ...
   9  | 1,  154,   802,  1792,   2962,   4312,   5842,   7552,   9442,  11512, ...
  10  | 1,  220,   590,   690,    790,    890,    990,   1090,   1190,   1290, ...
  11  | 1,  375,  2091,  4643,   7635,  11067,  14939,  19251,  24003,  29195, ...
  12  | 1,  444,   948,   948,    948,    948,    948,    948,    948,    948, ...
  13  | 1,  781,  5461, 14119,  24727,  37285,  51793,  68251,  86659, 107017, ...
  14  | 1,  952,  3066,  4046,   5026,   6006,   6986,   7966,   8946,   9926, ...
  15  | 1, 1456,  9361, 22756,  40186,  61066,  85396, 113176, 144406, 179086, ...
  16  | 1, 1696,  6096,  8240,   9520,  10800,  12080,  13360,  14640,  15920, ...
  17  | 1, 2500, 18225, 49131,  90883, 143175, 206007, 279379, 363291, 457743, ...
  18  | 1, 2466,  7344, 10872,  14166,  16866,  19566,  22266,  24966,  27666, ...
  19  | 1, 4029, 29356, 77616, 140316, 217456, 309036, 415056, 535516, 670416, ...
  20  | 1, 4500, 19580, 31620,  39820,  48020,  56220,  64420,  72620,  80820, ...
  21  | 1, 6175, 40720, 97336, 168022, 252778, 351604, 464500, 591466, 732502, ...
  22  | 1, 6820, 31042, 52030,  65890,  79750,  93610, 107470, 121330, 135190, ...
.

B. Poonen and M. Rubinstein, The Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics 11, no. 1 (1998), pp. 135-156; DOI:10.1137/S0895480195281246. [Author's copy]. The latest arXiv version arXiv:math/9508209 has corrected some typos in the published version.
Scott R. Shannon, Extended Table of A350000 for 5 <= n <= 46, Dec 22, 2021 [This shows the initial terms of the rows in human order (not by antidiagonals)]
Scott R. Shannon, Illustration for T(9,1)
Scott R. Shannon, T(9,2)
Scott R. Shannon, T(9,3)
Scott R. Shannon, T(9,4)
Scott R. Shannon, T(10,1)
Scott R. Shannon, T(10,2)
Scott R. Shannon, T(10,3)
Scott R. Shannon, T(11,1)
Scott R. Shannon, T(11,2)
Scott R. Shannon, T(11,3)
Scott R. Shannon, T(14,1)
Scott R. Shannon, T(14,2)
Scott R. Shannon, T(14,3)
Scott R. Shannon, T(17,3)
Scott R. Shannon, T(29,1)
Scott R. Shannon, Close-up of the 11-gon in T(29,1)
Scott R. Shannon, Close-up of a 9-gon in T(29,2). This shows the mitosis of the 11-gon from generation 1 in the previous image -- it has formed one 9-gon, five 7-gons, twelve 6-gons and numerous other 5, 4, and 3-gons.
Scott R. Shannon, Zoomed-in view of T(51,2). This shows the complicated structure formed after just 2 generations, typical of larger values of n.
N. J. A. Sloane, Rough sketch of first few generations of mitosis of a triangle, square, pentagon, and hexagon. The central pentagonal cell of the pentagon splits into 10 triangles and a pentagon at every generation, with the cells getting smaller and smaller. The third splitting is drawn in red ink. The second splitting of the hexagon is also drawn in red ink, but then all the cells are triangles, and no further mitosis takes place.

Cf. A007678 (column 1), A349807 (column 2), A017281 (row 5), A349808 (row 7); also A350501, A350502.

Cf. also A331450, A349967, A349968.

Formulas for the initial rows: (These are easy to prove.)
To avoid double subscripts, we use a(k) for T(n,k) when we are looking at row n.
n=3: a(k) = 1, for k >= 0.
n=4: a(0) = 1, a(k) = 4 for k >= 1.
n=5: a(k) = 10k+1, k >= 0. See A017281.
n=6: a(0) = 1, a(1) = 24, a(k) = 42 for k >= 2.
n=7: a(0) = 1, a(k) = 35*k^2+35*k-20 for k >= 1. See A349808.
n=8: a(0) = 1, a(1) = 80, a(k) = 152 for k >= 2.
n=9: a(0) = 1, a(1) = 154, a(k) = 90*k^2+540*k-638 for k >= 2.
n=10: a(0) = 1, a(1) = 220, a(k) = 100*k+390 for k >= 2.
n=11: a(0) = 1, a(1) = 375, a(k) = 220*k^2 + 1452*k - 1693 for k >= 2.
n=12: a(0) = 1, a(1) = 444, a(k) = 948 for k >= 2.
n=13: a(0) = 1, a(1) = 781, a(k) = 975*k^2 + 3783*k - 6005 for k >= 2.
n=14: a(0) = 1, a(k) = 980*k + 1106 for k >= 1.
n=15: a(k) = 1725*k^2+5355*k-8834 for k >= 3.
n=16: a(k) = 1280*k + 4400 for k >= 3.
n=18: a(k) = 2700*k + 3366 for k >= 4.
Also T(n,1) = A007678(n).

A161709 a(n) = 22*n + 1.

Original entry on oeis.org

1, 23, 45, 67, 89, 111, 133, 155, 177, 199, 221, 243, 265, 287, 309, 331, 353, 375, 397, 419, 441, 463, 485, 507, 529, 551, 573, 595, 617, 639, 661, 683, 705, 727, 749, 771, 793, 815, 837, 859, 881, 903, 925, 947, 969, 991, 1013, 1035, 1057, 1079, 1101, 1123

Offset: 0

Reinhard Zumkeller, Jun 17 2009

Italo Ghersi, Matematica dilettevole e curiosa, p. 139, Hoepli, Milano, 1967. [From Vincenzo Librandi, Dec 02 2009]

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005408, A008604, A016813, A016921, A017281, A017533, A128470, A158057, A161700, A161705, A161714.

List([0..60], n-> 1+22*n ); # G. C. Greubel, Sep 18 2019

[1+22*n: n in [0..60]]; // G. C. Greubel, Sep 18 2019

seq(1+22*n, n=0..60); # G. C. Greubel, Sep 18 2019

22*Range[0,60]+1 (* Harvey P. Dale, Jan 09 2011 *)

vector(60, n, 22*n-21) \\ G. C. Greubel, Sep 18 2019

[1+22*n for n in (0..60)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (1 + 21*x)/(1-x)^2.
E.g.f.: (1 + 22*x)*exp(x). (End)

A139222 a(n) = 30*n - 27.

Original entry on oeis.org

3, 33, 63, 93, 123, 153, 183, 213, 243, 273, 303, 333, 363, 393, 423, 453, 483, 513, 543, 573, 603, 633, 663, 693, 723, 753, 783, 813, 843, 873, 903, 933, 963, 993, 1023, 1053, 1083, 1113, 1143, 1173, 1203, 1233, 1263, 1293, 1323, 1353, 1383, 1413, 1443, 1473

Offset: 1

Odimar Fabeny, Jun 06 2008

Multiples of 3 with the units digit equal to 3.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Subsequence of A034709, together with A017281, A017293, A139245, A017329, A139249, A139264, A139279 and A139280.

[30*n - 27: n in [1..60]]; // Vincenzo Librandi, Jun 17 2011

Range[3, 2000, 30] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)
30*Range[50]-27 (* or *) NestList[30+#&,3,50] (* Harvey P. Dale, Mar 27 2021 *)

a(n)=30*n-27 \\ Charles R Greathouse IV, Aug 25 2014

a(n) = a(n-1) + 30.
From Elmo R. Oliveira, Apr 04 2025: (Start)
G.f.: 3*x*(1+9*x)/(1-x)^2.
E.g.f.: 3*(exp(x)*(10*x - 9) + 9).
a(n) = 3*A017281(n-1) = A139280(n)/3.
a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)

More terms from Reinhard Zumkeller, Jun 22 2008

A139249 a(n) = 30*n - 24.

Original entry on oeis.org

6, 36, 66, 96, 126, 156, 186, 216, 246, 276, 306, 336, 366, 396, 426, 456, 486, 516, 546, 576, 606, 636, 666, 696, 726, 756, 786, 816, 846, 876, 906, 936, 966, 996, 1026, 1056, 1086, 1116, 1146, 1176, 1206, 1236, 1266, 1296, 1326, 1356, 1386, 1416, 1446, 1476

Offset: 1

Odimar Fabeny, Jun 06 2008, Jun 07 2008

Multiples of 6 with unit digit equal to 6.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Subsequence of A034709, together with A017281, A017293, A139222, A139245, A017329, A139264, A139279 and A139280. - Reinhard Zumkeller, Jun 22 2008

Cf. A016861.

[30*n - 24: n in [1..60]]; // Vincenzo Librandi, Jun 19 2011

Range[6,7000,30] (* Vladimir Joseph Stephan Orlovsky, Jun 18 2011 *)
NestList[30+#&,6,50] (* or *) LinearRecurrence[{2,-1},{6,36},50] (* Harvey P. Dale, May 27 2018 *)

a(n)=30*n-24 \\ Charles R Greathouse IV, Aug 25 2014

a(n) = a(n-1) + 30.
From Elmo R. Oliveira, Apr 04 2025: (Start)
G.f.: 6*x*(1+4*x)/(1-x)^2.
E.g.f.: 6*(exp(x)*(5*x - 4) + 4).
a(n) = 6*A016861(n-1).
a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)

More terms from Reinhard Zumkeller, Jun 22 2008

Edited by R. J. Mathar, Jul 20 2008

A139264 a(n) = 70*n - 63.

Original entry on oeis.org

7, 77, 147, 217, 287, 357, 427, 497, 567, 637, 707, 777, 847, 917, 987, 1057, 1127, 1197, 1267, 1337, 1407, 1477, 1547, 1617, 1687, 1757, 1827, 1897, 1967, 2037, 2107, 2177, 2247, 2317, 2387, 2457, 2527, 2597, 2667, 2737, 2807, 2877, 2947, 3017, 3087, 3157, 3227

Offset: 1

Odimar Fabeny, Jun 06 2008

Multiples of 7 with unit digit equal to 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Subsequence of A034709, together with A017281, A017293, A139222, A139245, A017329, A139249, A139279 and A139280.

[70*n-63: n in [1..50]]; // Vincenzo Librandi, Jun 19 2011

70*Range[50]-63 (* Harvey P. Dale, May 06 2019 *)

a(n)=70*n-63 \\ Charles R Greathouse IV, Aug 25 2014

a(n) = a(n-1) + 70.
From Elmo R. Oliveira, Apr 04 2025: (Start)
G.f.: 7*x*(1+9*x)/(1-x)^2.
E.g.f.: 7*(exp(x)*(10*x - 9) + 9).
a(n) = 7*A017281(n-1).
a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)

More terms from Reinhard Zumkeller, Jun 22 2008

A161714 a(n) = 28*n + 1.

Original entry on oeis.org

1, 29, 57, 85, 113, 141, 169, 197, 225, 253, 281, 309, 337, 365, 393, 421, 449, 477, 505, 533, 561, 589, 617, 645, 673, 701, 729, 757, 785, 813, 841, 869, 897, 925, 953, 981, 1009, 1037, 1065, 1093, 1121, 1149, 1177, 1205, 1233, 1261, 1289, 1317, 1345, 1373

Offset: 0

Reinhard Zumkeller, Jun 17 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005408, A016813, A016921, A017281, A017533, A128470, A158057, A161700, A161705, A161709.

List([0..60], n-> 1+28*n); # G. C. Greubel, Sep 18 2019

[28*n + 1: n in [0..60]]; // Vincenzo Librandi, May 04 2011

seq(1+28*n, n=0..60); # G. C. Greubel, Sep 18 2019

Range[1, 1700, 28] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)
CoefficientList[Series[(1+27x)/(1-x)^2, {x,0,60}], x] (* Michael De Vlieger, Apr 05 2017 *)

vector(60, n, 28*n-27) \\ G. C. Greubel, Sep 18 2019

[1+28*n for n in (0..60)] # G. C. Greubel, Sep 18 2019

G.f.: (1 + 27*x)/(1-x)^2. - Indranil Ghosh, Apr 05 2017

E.g.f.: (1 + 28*x)*exp(x). - G. C. Greubel, Sep 18 2019

A062332 Primes starting and ending with 1.

Original entry on oeis.org

11, 101, 131, 151, 181, 191, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291, 1301, 1321, 1361, 1381, 1451, 1471, 1481, 1511, 1531, 1571, 1601, 1621, 1721, 1741, 1801, 1811, 1831, 1861, 1871, 1901, 1931, 1951, 10061, 10091, 10111, 10141

Offset: 1

Amarnath Murthy, Jun 21 2001

Complement of A208261 (nonprime numbers with all divisors starting and ending with digit 1) with respect to A208262 (numbers with all divisors starting and ending with digit 1). - Jaroslav Krizek, Mar 04 2012

Intersection of A030430 and A045707. - Michel Marcus, Jun 08 2013

			102701 is a member as it is a prime and the first and the last digits are both 1.

Harry J. Smith, Table of n, a(n) for n = 1..1000

Cf. A208259 (Numbers starting and ending with digit 1).

Cf. A010051, A017281, A131835, A000030.

a062332 n = a062332_list !! (n-1)
a062332_list = filter ((== 1) . a010051') a208259_list
-- Reinhard Zumkeller, Jul 16 2014

fl1Q[n_]:=Module[{idn=IntegerDigits[n]},First[idn]==Last[idn]==1]; Select[ Prime[Range[1300]],fl1Q] (* Harvey P. Dale, Apr 30 2012 *)

{ n=-1; t=log(10); forprime (p=2, 5*10^5, if ((p-10*(p\10)) == 1 && (p\10^(log(p)\t)) == 1, write("b062332.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

A010051(a(n)) * A000030(a(n)) * (a(n) mod 10) = 1. - Reinhard Zumkeller, Jul 16 2014

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 29 2001

Missing term a(36)=1901 added by Harry J. Smith, Aug 05 2009

A086273 Rectangular array T(n,k) of central polygonal numbers, by antidiagonals.

Original entry on oeis.org

1, 1, 3, 1, 4, 7, 1, 5, 10, 13, 1, 6, 13, 19, 21, 1, 7, 16, 25, 31, 31, 1, 8, 19, 31, 41, 46, 43, 1, 9, 22, 37, 51, 61, 64, 57, 1, 10, 25, 43, 61, 76, 85, 85, 73, 1, 11, 28, 49, 71, 91, 106, 113, 109, 91, 1, 12, 31, 55, 81, 106, 127, 141, 145, 136, 111, 1, 13, 34, 61, 91, 121, 148

Offset: 1

Clark Kimberling, Jul 14 2003

Transpose of the array at A086272.

			Northwest corner:
  1    1    1    1    1    1    1    1    1    1
  3    4    5    6    7    8    9   10   11   12 A000027
  7   10   13   16   19   22   25   28   31   34 A112414, A016777
  13   19   25   31   37   43   49   55   61   67 A016921
  21   31   41   51   61   71   81   91  101  111 A017281
  31   46   61   76   91  106  121  136  151  166
  43   64   85  106  127  148  169  190  211  232
  57   85  113  141  169  197  225  253  281  309
  73  109  145  181  217  253  289  325  361  397
  91  136  181  226  271  316  361  406  451  496
111  166  221  276  331  386  441  496  551  606
133  199  265  331  397  463  529  595  661  727
157  235  313  391  469  547  625  703  781  859
183  274  365  456  547  638  729  820  911 1002
211  316  421  526  631  736  841  946 1051 1156
241  361  481  601  721  841  961 1081 1201 1321

Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7 (2004) # 04.1.6.

Cf. A086270, A086271, A086272, A086274.

A086273 := proc(n,k) (k+1)*n*(n-1)/2+1 ; end proc: # R. J. Mathar, Jun 05 2011

T(n, k)=(k+1)*binomial(n, 2)+1.

A144433 Multiples of 8 interleaved with the sequence of odd numbers >= 3.

Original entry on oeis.org

8, 3, 16, 5, 24, 7, 32, 9, 40, 11, 48, 13, 56, 15, 64, 17, 72, 19, 80, 21, 88, 23, 96, 25, 104, 27, 112, 29, 120, 31, 128, 33, 136, 35, 144, 37, 152, 39, 160, 41, 168, 43, 176, 45, 184, 47, 192, 49, 200, 51, 208, 53, 216, 55, 224, 57, 232, 59, 240, 61, 248, 63, 256, 65, 264

Offset: 1

Paul Curtz, Oct 04 2008

For n >= 2, these are the numerators of 1/n^2 - 1/(n+1)^2: A061037(4), A061039(5), A061041(6), A061043(7), A061045(8), A061047(9), A061049(10), etc.

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A120070.

[5+3/2*(-1)^(n-1)*(n-1)+3*(-1)^(n-1)+5/2*(n-1): n in [1..70]]; // Vincenzo Librandi, Jul 30 2011

A144433:=n->(n+1)*4^(n mod 2); seq(A144433(n), n=1..100); # Wesley Ivan Hurt, Nov 27 2013

Table[(n + 1)* 4^Mod[n, 2], {n, 100}] (* Wesley Ivan Hurt, Nov 27 2013 *)

x='x+O('x^50); Vec( x*(8+3*x-x^3)/((1-x)^2*(1+x)^2)) \\ G. C. Greubel, Sep 19 2018

a(2*n+1) = A008590(n+1), a(2*n) = A005408(n).
a(2*n+1) + a(2*n+2) = A017281(n+1).
From R. J. Mathar, Apr 01 2009: (Start)
a(n) = 2*a(n-2) - a(n-4).
G.f.: x*(8+3*x-x^3)/((1-x)^2*(1+x)^2). (End)
a(n) = (n + 1) * 4^(n mod 2). - Wesley Ivan Hurt, Nov 27 2013

Edited by R. J. Mathar, Apr 01 2009

cp's OEIS Frontend

A017282 a(n) = (10*n + 1)^2.

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A350000 Table read by antidiagonals: T(n,k) (n >= 3, k >= 0) is the number of cells in a regular n-gon after k generations of mitosis.

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A161709 a(n) = 22*n + 1.

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A139222 a(n) = 30*n - 27.

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Magma

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A139249 a(n) = 30*n - 24.

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A139264 a(n) = 70*n - 63.

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A161714 a(n) = 28*n + 1.

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