A016850 -id:A016850 - cp's OEIS frontend

A244630 a(n) = 17*n^2.

0, 17, 68, 153, 272, 425, 612, 833, 1088, 1377, 1700, 2057, 2448, 2873, 3332, 3825, 4352, 4913, 5508, 6137, 6800, 7497, 8228, 8993, 9792, 10625, 11492, 12393, 13328, 14297, 15300, 16337, 17408, 18513, 19652, 20825, 22032, 23273, 24548, 25857, 27200, 28577, 29988

Offset: 0

Vincenzo Librandi, Jul 03 2014

First bisection of A195047. - Bruno Berselli, Jul 03 2014

Norms of purely imaginary numbers in Z[sqrt(-17)] (for example, 3*sqrt(-17) has norm 153). - Alonso del Arte, Jun 23 2018

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

Cf. A008599, A195047.

Cf. similar sequences of the type k*n^2: A000290 (k = 1), A001105 (k = 2), A033428 (k = 3), A016742 (k = 4), A033429 (k = 5), A033581 (k = 6), A033582 (k = 7), A139098 (k = 8), A016766 (k = 9), A033583 (k = 10), A033584 (k = 11), A135453 (k = 12), A152742 (k = 13), A144555 (k = 14), A064761 (k = 15), A016802 (k = 16), this sequence (k = 17), A195321 (k = 18), A244631 (k = 19), A195322 (k = 20), A064762 (k = 21), A195323 (k = 22), A244632 (k = 23), A195824 (k = 24), A016850 (k = 25), A244633 (k = 26), A244634 (k = 27), A064763 (k = 28), A244635 (k = 29), A244636 (k = 30).

List([0..45],n->17*n^2); # Muniru A Asiru, Jun 29 2018

Magma
```
[17*n^2: n in [0..40]];
```

seq(17*n^2,n=0..45); # Muniru A Asiru, Jun 29 2018

Mathematica
```
Table[17 n^2, {n, 0, 40}]
```

a(n)=17*n^2 \\ Charles R Greathouse IV, Oct 07 2015

for (i <- 0 to 50) yield 17 * (i * i) // Alonso del Arte, Jun 29 2018

G.f.: 17*x*(1 + x)/(1 - x)^3. [corrected by Bruno Berselli, Jul 03 2014]
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = 17*A000290(n). - Omar E. Pol, Jul 03 2014
a(n) = a(-n). - Muniru A Asiru, Jun 29 2018
From Elmo R. Oliveira, Dec 02 2024: (Start)
E.g.f.: 17*x*(1 + x)*exp(x).
a(n) = n*A008599(n) = A195047(2*n). (End)

A016910 a(n) = (6*n)^2.

Original entry on oeis.org

0, 36, 144, 324, 576, 900, 1296, 1764, 2304, 2916, 3600, 4356, 5184, 6084, 7056, 8100, 9216, 10404, 11664, 12996, 14400, 15876, 17424, 19044, 20736, 22500, 24336, 26244, 28224, 30276, 32400, 34596, 36864, 39204, 41616, 44100, 46656, 49284, 51984, 54756, 57600, 60516, 63504, 66564, 69696, 72900

Offset: 0

N. J. A. Sloane

Areas A of two classes of triangles with integer sides (a,b,c) where a = 9k, b=10k and c = 17k, or a = 3k, b = 25k and c = 26k for k=0,1,2,... These areas are given by Heron's formula A = sqrt(s(s-a)(s-b)(s-c)) = (6k)^2, with the semiperimeter s = (a+b+c)/2. This sequence is a subsequence of A188158. - Michel Lagneau, Oct 11 2013

Sequence found by reading the line from 0, in the direction 0, 36, ..., in the square spiral whose vertices are the generalized 20-gonal numbers A218864. - Omar E. Pol, May 13 2018.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A089491, A188158, A243941.

Cf. similar sequences of the type k*n^2: A000290 (k=1), A001105 (k=2), A033428 (k=3), A016742 (k=4), A033429 (k=5), A033581 (k=6), A033582 (k=7), A139098 (k=8), A016766 (k=9), A033583 (k=10), A033584 (k=11), A135453 (k=12), A152742 (k=13), A144555 (k=14), A064761 (k=15), A016802 (k=16), A244630 (k=17), A195321 (k=18), A244631 (k=19), A195322 (k=20), A064762 (k=21), A195323 (k=22), A244632 (k=23), A195824 (k=24), A016850 (k=25), A244633 (k=26), A244634 (k=27), A064763 (k=28), A244635 (k=29), A244636 (k=30).

[(6*n)^2: n in [0..40]]; // Vincenzo Librandi, May 03 2011

(6*Range[0,40])^2 (* or *) LinearRecurrence[{3,-3,1},{0,36,144},40] (* Harvey P. Dale, Dec 25 2017 *)
Table[36 n^2, {n, 0, 45}] (* Omar E. Pol, Jun 07 2018 *)

a(n)=36*n^2 \\ Charles R Greathouse IV, Jun 10 2016

From Ilya Gutkovskiy, Jun 09 2016: (Start)
O.g.f.: 36*x*(1 + x)/(1 - x)^3.
E.g.f.: 36*x*(1 + x)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=1} 1/a(n) = Pi^2/216 = A086726. (End)
Product_{n>=1} a(n)/A136017(n) = Pi/3. - Fred Daniel Kline, Jun 09 2016
a(n) = t(9*n) - 9*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(9*n) - 9*A000217(n). - Bruno Berselli, Aug 31 2017
a(n) = 36*A000290(n) = 18*A001105(n) = 12*A033428 = 9*A016742(n) = 6*A033581(n) = 4*A016766(n) = 3*A135453(n) = 2*A195321(n). - Omar E. Pol, Jun 07 2018
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/432. - Amiram Eldar, Jun 27 2020
From Amiram Eldar, Jan 25 2021: (Start)
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/6)/(Pi/6).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/6)/(Pi/6) = 3/Pi (A089491). (End)

A017222 a(n) = (9*n + 5)^2.

Original entry on oeis.org

25, 196, 529, 1024, 1681, 2500, 3481, 4624, 5929, 7396, 9025, 10816, 12769, 14884, 17161, 19600, 22201, 24964, 27889, 30976, 34225, 37636, 41209, 44944, 48841, 52900, 57121, 61504, 66049, 70756

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+5)^2: A010864 (m=0), A000290 (m=1), A016754 (m=2), A016790 (m=3), A016814 (m=4), A016850 (m=5), A016970 (m=6), A017042 (m=7), A017126 (m=8), this sequence (m=9), A017330 (m=10), A017450 (m=11), A017582 (m=12).

Cf. A017221, A017246.

[(9*n+5)^2: n in [0..35]]; // Vincenzo Librandi, Jul 24 2011

(9Range[0,30]+5)^2 (* or *) LinearRecurrence[{3,-3,1},{25,196,529},30] (* Harvey P. Dale, May 22 2012 *)

a(n)=(9*n+5)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(9*n+5)^2 for n in range(41)] # G. C. Greubel, Dec 29 2022

a(n) = A017221(n)^2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 22 2012
G.f.: (25 + 121*x + 16*x^2)/(1-x)^3. - R. J. Mathar, Mar 20 2018
From G. C. Greubel, Dec 29 2022: (Start)
a(2*n+1) = 4*A017246(n).
a(n) = a(n-1) + 9*(18*n + 1).
E.g.f.: (25 + 171*x + 81*x^2)*exp(x). (End)

A017270 a(n) = (10*n)^2.

Original entry on oeis.org

0, 100, 400, 900, 1600, 2500, 3600, 4900, 6400, 8100, 10000, 12100, 14400, 16900, 19600, 22500, 25600, 28900, 32400, 36100, 40000, 44100, 48400, 52900, 57600, 62500, 67600, 72900, 78400, 84100, 90000, 96100, 102400, 108900, 115600, 122500, 129600, 136900, 144400

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).

Cf. A000290, A008592, A016850.

[(10*n)^2: n in [0..40]]; // Vincenzo Librandi, Jul 28 2011

LinearRecurrence[{3,-3,1},{0,100,400},40] (* Harvey P. Dale, Oct 02 2017 *)

a(n)=(10*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = a(n-1) + 200*n - 100, n > 0 ; a(0)=0. - Miquel Cerda, Oct 30 2016
G.f.: 100*x*(1 + x)/(1 - x)^3. - Ilya Gutkovskiy, Oct 30 2016
a(n) = 100*A000290(n). - Michel Marcus, Oct 30 2016
From Amiram Eldar, Jan 25 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/600.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/1200.
Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/10)/(Pi/10).
Product_{n>=1} (1 - 1/a(n)) = sin(Pi/10)/(Pi/10) = 5*(sqrt(5)-1)/(2*Pi). (End)
From Elmo R. Oliveira, Nov 30 2024: (Start)
E.g.f.: 100*x*(1 + x)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = A008592(n)^2 = A000290(A008592(n)) = A016850(2*n). (End)

A016898 a(n) = (5*n + 4)^2.

Original entry on oeis.org

16, 81, 196, 361, 576, 841, 1156, 1521, 1936, 2401, 2916, 3481, 4096, 4761, 5476, 6241, 7056, 7921, 8836, 9801, 10816, 11881, 12996, 14161, 15376, 16641, 17956, 19321, 20736, 22201, 23716, 25281, 26896, 28561, 30276, 32041, 33856, 35721, 37636, 39601, 41616

Offset: 0

N. J. A. Sloane

If Y is a fixed 2-subset of a (5n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - Milan Janjic, Oct 21 2007

Interleaving of A017318 and A017378. - Michel Marcus, Aug 26 2015

			a(0) = (5*0 + 4)^2 = 16.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Milan Janjic, Two Enumerative Functions.
Eric Weisstein's MathWorld, Polygamma Function.
Wikipedia, Polygamma Function.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016850, A016862, A016874, A016886.

[(5*n+4)^2: n in [0..70]]; // Vincenzo Librandi, May 02 2011

Table[(5*n + 4)^2, {n, 0, 25}] (* Amiram Eldar, Oct 02 2020 *)
LinearRecurrence[{3,-3,1},{16,81,196},50] (* Harvey P. Dale, Jul 30 2023 *)

Vec((16 + 33*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Mar 30 2017

From Colin Barker, Mar 30 2017: (Start)
G.f.: (16 + 33*x + x^2) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
Sum_{n>=0} 1/a(n) = polygamma(1, 4/5)/25. - Amiram Eldar, Oct 02 2020

A156701 a(n) = 4n^4 + 17n^2 + 4.

Original entry on oeis.org

4, 25, 136, 481, 1300, 2929, 5800, 10441, 17476, 27625, 41704, 60625, 85396, 117121, 157000, 206329, 266500, 339001, 425416, 527425, 646804, 785425, 945256, 1128361, 1336900, 1573129, 1839400, 2138161, 2471956, 2843425, 3255304, 3710425

Offset: 0

Reinhard Zumkeller, Feb 13 2009

a(n) = A087475(n)*A053755(n).

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A016850, A053755, A087475, A099761.

[4*n^4+17*n^2+4: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Table[4n^4+17n^2+4,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{4,25,136,481,1300},50] (* Harvey P. Dale, Nov 08 2017 *)

a(n)=4*n^4+17*n^2+4 \\ Charles R Greathouse IV, Oct 21 2022

a(n) = (2*(n^2 - 1))^2 + (5*n)^2.
G.f.: (-4-25*x^4-11*x^3-51*x^2-5*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009
E.g.f.: exp(x)*(4 + 21*x + 45*x^2 + 24*x^3 + 4*x^4). - Stefano Spezia, Jul 08 2023

A010015 a(0) = 1, a(n) = 25*n^2 + 2 for n > 0.

Original entry on oeis.org

1, 27, 102, 227, 402, 627, 902, 1227, 1602, 2027, 2502, 3027, 3602, 4227, 4902, 5627, 6402, 7227, 8102, 9027, 10002, 11027, 12102, 13227, 14402, 15627, 16902, 18227, 19602, 21027, 22502, 24027, 25602, 27227, 28902, 30627, 32402, 34227, 36102, 38027, 40002

Offset: 0

N. J. A. Sloane

Subsequence of A160842. - Bruno Berselli, Feb 06 2012

The identity (25*n^2 + 1)^2 - (25*n^2 + 2)*(5*n)^2 = 1 can be written as (A016850(n+1) + 1)^2 - a(n+1)*A008587(n+1)^2 = 1. - Vincenzo Librandi, Feb 08 2012

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

Cf. A206399.

Join[{1}, 25 Range[40]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {27, 102, 227}, 50]] (* Vincenzo Librandi, Feb 08 2012 *)

A010015(n)=25*n^2+2-!n \\ M. F. Hasler, Feb 14 2012

G.f.: (1+x)*(1 + 23*x + x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*25 + 2)*e^x - 1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) =3/4+sqrt(2)/20*Pi*coth(Pi*sqrt(2)/5) = 1.062575323280590.. - R. J. Mathar, May 07 2024
a(n) = A262221(n)+A262221(n+1). - R. J. Mathar, May 07 2024

A133496 a(n) = (29*n)^2.

Original entry on oeis.org

0, 841, 3364, 7569, 13456, 21025, 30276, 41209, 53824, 68121, 84100, 101761, 121104, 142129, 164836, 189225, 215296, 243049, 272484, 303601, 336400, 370881, 407044, 444889, 484416, 525625, 568516, 613089, 659344, 707281, 756900, 808201

Offset: 0

Richard Choulet, Dec 23 2007

			a(1) = 29^2 = 841, a(2) = 58^2 = 3364, a(3) = 87^2 = 7569.

Vincenzo Librandi, Table of n, a(n) for n = 0..750
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A016850.

[(29*n)^2: n in [0..50]]; // Vincenzo Librandi, Apr 26 2011

a(n)=(29*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

G.f.: -841*x*(1+x) / (x-1)^3 . - R. J. Mathar, Mar 13 2015

More terms from Philippe Deléham, Dec 21 2008

a(12) corrected by Vincenzo Librandi, Apr 26 2011

A232329 Integer areas A of the integer-sided triangles such that the product of the inradius and the circumradius is a square.

Original entry on oeis.org

42, 168, 378, 672, 1050, 1512, 2058, 2088, 2688, 3000, 3402, 4200, 5082, 6048, 6960, 7098, 8232, 8352, 9450, 10752, 12000, 12138, 13608, 15162, 16800, 18522, 18792, 20328, 22218, 24192, 26250, 27000, 27840, 28392, 30618, 31416, 32928, 33408, 35322, 36000, 37800, 40362

Offset: 1

Michel Lagneau, Nov 22 2013

The areas of the primitive triangles of sides (a, b, c) and inradius, circumradius equals respectively to r and R are 42, 3000,...  The sides of the nonprimitive triangles are of the form (a*k, b*k, c*k) with r’ = r*k and R’=R*k where r’, R’ are respectively the inradius and the circumradius of the nonprimitive triangles. The areas A’ of the nonprimitive triangles are A’ = A*k^2. The set {A016850} (numbers (5n)^2) is included in the set of the products r*R (see the table below).
The area A of a triangle whose sides have lengths a, b, and c is given by Heron's formula: A = sqrt(s*(s-a)*(s-b)*(s-c)), where s = (a+b+c)/2. The inradius r is given by r = A/s and the circumradius is given by R = abc/4A.
The product r*R is given by r*R = abc/2(a+b+c).
The following table gives the first values (A, a, b, c, r, R, r*R).
  -----------------------------------------------------
  |    A  |   a  |   b |   c   |   r  |   R    | r*R  |
  -----------------------------------------------------
  |    42 |   7  |  15  |  20  |    2 |  25/2  |  5^2 |
  |   168 |  14  |  30  |  40  |    4 |  25    | 10^2 |
  |   378 |  21  |  45  |  60  |    6 |  75/2  | 15^2 |
  |   672 |  28  |  60  |  80  |    8 |  50    | 20^2 |
  |  1050 |  35  |  75  | 100  |   10 | 125/2  | 25^2 |
  |  1512 |  42  |  90  | 120  |   12 |  75    | 30^2 |
  |  2058 |  49  | 105  | 140  |   14 | 175/2  | 35^2 |
  |  2688 |  56  | 120  | 160  |   16 | 100    | 40^2 |
  |  3000 |  80  |  85  |  85  |   24 | 289/6  | 34^2 |
  |  3402 |  63  | 135  | 180  |   18 | 225/2  | 45^2 |
  |  4200 |  70  | 150  | 200  |   20 | 125    | 50^2 |
  |  5082 |  77  | 165  | 220  |   22 | 275/2  | 55^2 |
  |  6048 |  84  | 180  | 240  |   24 | 150    | 60^2 |
  |  6960 |  58  | 300  | 338  |   20 | 845/4  | 65^2 |
  |  7098 |  91  | 195  | 260  |   26 | 325/2  | 65^2 |
  ....................................................

			a(1) = 42 because, for (a,b,c) = (7, 15, 20):
  the semiperimeter s = (7+15+20)/2 =21, and
  A = sqrt(21*(21-7)*(21-15)*(21-20)) = 42
  R = abc/4A = 7*15*20/(4*42) = 25/2
  r = A/s = 42/21 = 2, hence r*R = 25 is a square.

Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32.

Zak Seidov, Table of n, a(n) for n = 1..100
Zak Seidov, Table of 814 values of area A, sides a>=b>=c, semiprime s, and sqrt(Rr), in the order of increasing "a" from 20 up to 10000.
Mohammad K. Azarian, Solution to Problem S125: Circumradius and Inradius, Math Horizons, Vol. 16, Issue 2, November 2008, p. 32.
Eric Weisstein's World of Mathematics, Circumradius
Eric Weisstein's World of Mathematics, Inradius

Cf. A016850, A188158, A208984, A232274.

nn=800;lst={};Do[s=(a+b+c)/2;rr=a*b*c/(2*(a+b+c))
;If[IntegerQ[s],area2=s(s-a)(s-b)(s-c);If[0

lista(nn)=lst=[]; for (a = 1, nn, for (b=1, a, for (c=1, b, s=(a+b+c)/2; rr=a*b*c/(2*(a+b+c)); if ((type(s) == "t_INT") && (type(rr) == "t_INT"), area2=s*(s-a)*(s-b)*(s-c); if ((0Michel Marcus, Jun 09 2015

{for(a=20,10000,forstep(b=a,2,-1,forstep(c=min(b,a+b-1),a-b+1,-1,if((a+b+c)%2<1,s=(a+b+c)/2;if(issquare(s*(s-a)*(s-b)*(s-c),&A),
if((a*b*c)%(2*(a+b+c))<1&&if(issquare(a*b*c/(2*(a+b+c)),&d),
print([A,a,b,c,s,d]))))))))} \\ Faster version used for afile. Zak Seidov, Jun 06 2015

Missing term 33408 added by Zak Seidov, Jun 08 2015

A303302 a(n) = 34*n^2.

Original entry on oeis.org

0, 34, 136, 306, 544, 850, 1224, 1666, 2176, 2754, 3400, 4114, 4896, 5746, 6664, 7650, 8704, 9826, 11016, 12274, 13600, 14994, 16456, 17986, 19584, 21250, 22984, 24786, 26656, 28594, 30600, 32674, 34816, 37026, 39304, 41650, 44064, 46546, 49096, 51714, 54400, 57154, 59976, 62866, 65824, 68850, 71944

Offset: 0

Omar E. Pol, May 13 2018

Sequence found by reading the line from 0, in the direction 0, 34, ..., in the square spiral whose vertices are the generalized 19-gonal numbers A303813.

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

Cf. A005843, A008599, A303813.

Cf. similar sequences of the type k*n^2: A000290 (k=1), A001105 (k=2), A033428 (k=3), A016742 (k=4), A033429 (k=5), A033581 (k=6), A033582 (k=7), A139098 (k=8), A016766 (k=9), A033583 (k=10), A033584 (k=11), A135453 (k=12), A152742 (k=13), A144555 (k=14), A064761 (k=15), A016802 (k=16), A244630 (k=17), A195321 (k=18), A244631 (k=19), A195322 (k=20), A064762 (k=21), A195323 (k=22), A244632 (k=23), A195824 (k=24), A016850 (k=25), A244633 (k=26), A244634 (k=27), A064763 (k=28), A244635 (k=29), A244636 (k=30), A244082 (k=32), this sequence (k=34), A016910 (k=36), A016982 (k=49), A017066 (k=64), A017162 (k=81), A017270 (k=100), A017390 (k=121), A017522 (k=144).

[34*n^2: n in [0..50]]; // Vincenzo Librandi Jun 07 2018

Table[34 n^2, {n, 0, 40}]
LinearRecurrence[{3,-3,1},{0,34,136},50] (* Harvey P. Dale, Jul 23 2018 *)

PARI
```
a(n) = 34*n^2;
```

concat(0, Vec(34*x*(1 + x) / (1 - x)^3 + O(x^40))) \\ Colin Barker, Jun 12 2018

a(n) = 34*A000290(n) = 17*A001105(n) = 2*A244630(n).
G.f.: 34*x*(1 + x)/(1 - x)^3. - Vincenzo Librandi, Jun 07 2018
From Elmo R. Oliveira, Dec 02 2024: (Start)
E.g.f.: 34*x*(1 + x)*exp(x).
a(n) = A005843(n)*A008599(n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

cp's OEIS Frontend

A244630 a(n) = 17*n^2.

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A016910 a(n) = (6*n)^2.

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A017222 a(n) = (9*n + 5)^2.

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Magma

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SageMath

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A017270 a(n) = (10*n)^2.

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Magma

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A016898 a(n) = (5*n + 4)^2.

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Magma

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A156701 a(n) = 4*n^4 + 17*n^2 + 4.

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A010015 a(0) = 1, a(n) = 25*n^2 + 2 for n > 0.

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A156701 a(n) = 4n^4 + 17n^2 + 4.