A014635 -id:A014635 - cp's OEIS frontend

A139274 a(n) = n(8n-1).

0, 7, 30, 69, 124, 195, 282, 385, 504, 639, 790, 957, 1140, 1339, 1554, 1785, 2032, 2295, 2574, 2869, 3180, 3507, 3850, 4209, 4584, 4975, 5382, 5805, 6244, 6699, 7170, 7657, 8160, 8679, 9214, 9765, 10332, 10915, 11514, 12129, 12760, 13407, 14070, 14749

Offset: 0

Omar E. Pol, Apr 26 2008

Sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the triangular numbers A000217.

Polygonal number connection: 2*P_n + 5*S_n where P_n is the n-th pentagonal number and S_n is the n-th square. - William A. Tedeschi, Sep 12 2010

			a(1) = 16*1 + 0 - 9 = 7; a(2) = 16*2 + 7 - 9 = 30; a(3) = 16*3 + 30 - 9 = 69. - _Vincenzo Librandi_, Aug 03 2010

G. C. Greubel, Table of n, a(n) for n = 0..5000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A139272, A139273, A139275, A139276, A139278, A139279, A139280, A139281, A139282.

[n*(8*n-1) : n in [0..50]]; // Wesley Ivan Hurt, Dec 04 2016

A139274:=n->n*(8*n-1): seq(A139274(n), n=0..100); # Wesley Ivan Hurt, Dec 04 2016

CoefficientList[Series[x (9 x + 7)/(1 - x)^3, {x, 0, 43}], x] (* Michael De Vlieger, Jan 11 2020 *)
Table[n(8n-1),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,7,30},50] (* Harvey P. Dale, Apr 01 2024 *)

a(n)=n*(8*n-1) \\ Charles R Greathouse IV, Jun 17 2017

Sequences of the form a(n) = 8*n^2 + c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n) = 3a(n-1) - 3a(n-2) + a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008
a(n) = 16*n + a(n-1) - 9 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(n) = (1/3) * Sum_{i=n..(7*n-1)} i. - Wesley Ivan Hurt, Dec 04 2016
From G. C. Greubel, Jul 18 2017: (Start)
G.f.: x*(9*x+7)/(1-x)^3.
E.g.f.: (8*x^2 + 7*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 4*log(2) + sqrt(2)*log(sqrt(2)+1) - (sqrt(2)+1)*Pi/2. - Amiram Eldar, Mar 18 2022

A134708 Even superperfect numbers divided by 2.

Original entry on oeis.org

1, 2, 8, 32, 2048, 32768, 131072, 536870912, 576460752303423488, 154742504910672534362390528, 40564819207303340847894502572032, 42535295865117307932921825928971026432

Offset: 1

Omar E. Pol, Nov 07 2007, Apr 23 2008

nonn

a(13) and a(14) have 157 and 183 digits respectively. - R. J. Mathar, Jan 07 2008
Largest proper divisor of n-th even superperfect number A061652(n). Also, largest proper divisor of n-th superperfect number A019279(n), if there are no odd superperfect numbers.
Indices of even hexagonal numbers (A014635) that are also even perfect numbers. - Omar E. Pol, Jan 11 2009

			a(5) = 2048 because the 5th even superperfect number is 4096 and 4096/2 = 2048.

Amiram Eldar, Table of n, a(n) for n = 1..18
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos [From _Omar E. Pol_, Jan 11 2009]

Cf. A019279, A061652, A133028.
Cf. A000043.
Cf. A032742, A138882, A139248.
Cf. A000217, A000396, A014635. - Omar E. Pol, Jan 11 2009

A000043 := proc(n) op(n,[2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213]) ; end: A061652 := proc(n) 2^(A000043(n)-1) ; end: A134708 := proc(n) A061652(n)/2 ; end: seq(A134708(n),n=1..14) ; # R. J. Mathar, Jan 07 2008

With[{max = 12}, 2^(MersennePrimeExponent[Range[max]] - 2)] (* Amiram Eldar, Oct 21 2024 *)

a(n) = A061652(n)/2.
a(n) = 2^(A000043(n)-2). - Omar E. Pol, Mar 01 2008
a(n) = A032742(A061652(n)). Also, a(n) = A032742(A019279(n)), if there are no odd superperfect numbers.
a(n) = Sum_{x=1..n-th superperfect number} x*(-1)^x. - Juri-Stepan Gerasimov, Jul 21 2009

More terms from R. J. Mathar, Jan 07 2008

A139276 a(n) = n(8n+3).

Original entry on oeis.org

0, 11, 38, 81, 140, 215, 306, 413, 536, 675, 830, 1001, 1188, 1391, 1610, 1845, 2096, 2363, 2646, 2945, 3260, 3591, 3938, 4301, 4680, 5075, 5486, 5913, 6356, 6815, 7290, 7781, 8288, 8811, 9350, 9905, 10476, 11063, 11666, 12285, 12920

Offset: 0

Omar E. Pol, Apr 26 2008

Sequence found by reading the line from 0, in the direction 0, 11,..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139272 in the same spiral.

			a(1)=16*1+0-5=11; a(2)=16*2+11-5=38; a(3)=16*3+38-5=81. - _Vincenzo Librandi_, Aug 03 2010

G. C. Greubel, Table of n, a(n) for n = 0..5000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A072279, A139272, A139273, A139274, A139275, A139277, A139278, A139279, A139280, A139281, A139282.

a[n_]:=n*(8*n+3); a[Range[0,60]] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
LinearRecurrence[{3,-3,1},{0,11,38},50] (* Harvey P. Dale, Jul 02 2022 *)

a(n)=n*(8*n+3) \\ Charles R Greathouse IV, Jun 16 2017

a(n) = 8*n^2 + 3*n.
Sequences of the form a(n)=8*n^2+c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n)= 3a(n-1)-3a(n-2)+a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008
a(n) = 16*n+a(n-1)-5 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From G. C. Greubel, Jul 18 2017: (Start)
G.f.: x*(5*x + 11)/(1-x)^3.
E.g.f.: (8*x^2 + 11*x)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 8/9 - (sqrt(2)-1)*Pi/6 - 4*log(2)/3 + sqrt(2)*log(sqrt(2)+1)/3. - Amiram Eldar, Mar 17 2022

A139277 a(n) = n(8n+5).

Original entry on oeis.org

0, 13, 42, 87, 148, 225, 318, 427, 552, 693, 850, 1023, 1212, 1417, 1638, 1875, 2128, 2397, 2682, 2983, 3300, 3633, 3982, 4347, 4728, 5125, 5538, 5967, 6412, 6873, 7350, 7843, 8352, 8877, 9418, 9975, 10548, 11137, 11742, 12363, 13000

Offset: 0

Omar E. Pol, Apr 26 2008

Sequence found by reading the line from 0, in the direction 0, 13, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A139273 in the same spiral.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250.

Cf. A139271, A139272, A139273, A139274, A139275, A139276, A139278, A139279, A139280, A139281, A139282.

Table[n (8 n + 5), {n, 0, 50}] (* Bruno Berselli, Aug 22 2018 *)
LinearRecurrence[{3,-3,1},{0,13,42},50] (* Harvey P. Dale, Dec 04 2018 *)

a(n)=n*(8*n+5) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 8*n^2 + 5*n.
Sequences of the form a(n) = 8*n^2 + c*n have generating functions x*{c+8 + (8-c)*x}/(1-x)^3 and recurrence a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008
a(n) = 16*n + a(n-1) - 3 for n > 0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
Sum_{n>=1} 1/a(n) = (sqrt(2)-1)*Pi/10 - 4*log(2)/5 + sqrt(2)*log(sqrt(2)+1)/5 + 8/25. - Amiram Eldar, Mar 18 2022
E.g.f.: exp(x)*x*(13 + 8*x). - Elmo R. Oliveira, Dec 15 2024

A181890 a(n) = 8n^2 + 14n + 5.

Original entry on oeis.org

5, 27, 65, 119, 189, 275, 377, 495, 629, 779, 945, 1127, 1325, 1539, 1769, 2015, 2277, 2555, 2849, 3159, 3485, 3827, 4185, 4559, 4949, 5355, 5777, 6215, 6669, 7139, 7625, 8127, 8645, 9179, 9729, 10295, 10877, 11475, 12089, 12719, 13365, 14027, 14705, 15399, 16109, 16835, 17577

Offset: 0

Paul Curtz, Feb 01 2011

A160050(4*n+1) = A033954(n); A160050(4*n+2) = A001107(n); the third quadrisection is a(n).
First 16 terms of clockwise spiral for odd numbers are as follows:
.
  13--15--17--19
   |           |
  11   1---3  21
   |       |   |
   9---7---5  23
               |
  31--29--27--25
.
a(n) comes from the third vertical.
Sequence found by reading the line from 5, in the direction 5, 27, in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Dec 25 2011

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

Cf. A000217, A001107, A014106, A014635, A033954, A064038, A160050.

[8*n^2+14*n+5: n in [0..700]]; // Vincenzo Librandi, Feb 01 2011

Table[(2n+1)(4n+5),{n,0,40}]  (* Harvey P. Dale, Feb 06 2011 *)
CoefficientList[Series[(5 + 12 x - x^2)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, May 23 2014 *)

a(n)=8*n^2+14*n+5 \\ Charles R Greathouse IV, Dec 21 2011

a(n) = A160050(4*n+3).
a(n) = (2*n+1)*(4*n+5).
a(n) = a(n-1) + 16*n + 6.
a(n) = 2*a(n-1) - a(n-2) + 16.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (5 + 12*x - x^2)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 25 2011
a(n) = A014635(n+1) - 1. - Omar E. Pol, Dec 25 2011
From Vaclav Kotesovec, Aug 18 2018: (Start)
Sum_{n>=0} 1/a(n) = 2/3 - Pi/12 - log(2)/6 = 0.289342748774193011891907697817...
Sum_{n>=0} (-1)^n / a(n) = (1 + sqrt(2))*Pi/12 - 2/3 - sqrt(2)*log(tan(Pi/8))/6 = 0.173114712692423461587883724528539... (End)
a(n) = A014106(2*n+1). - Rick L. Shepherd, Aug 06 2019
E.g.f.: (5 + 22*x + 8*x^2)*exp(x). - Elmo R. Oliveira, Oct 19 2024

A153798 a(n) = A000043(n)-2.

Original entry on oeis.org

0, 1, 3, 5, 11, 15, 17, 29, 59, 87, 105, 125, 519, 605, 1277, 2201, 2279, 3215, 4251, 4421, 9687, 9939, 11211, 19935, 21699, 23207, 44495, 86241, 110501, 132047, 216089, 756837, 859431, 1257785, 1398267, 2976219, 3021375, 6972591, 13466915, 20996009, 24036581

Offset: 1

Omar E. Pol, Jan 20 2009

nonn

Base 2 logarithm of A134708(n).

Amiram Eldar, Table of n, a(n) for n = 1..48

Cf. A000043, A014635, A134708.

MersennePrimeExponent[Range[48]] - 2 (* Amiram Eldar, Oct 17 2024 *)

a(40)-a(41) from Amiram Eldar, Oct 17 2024

A185438 a(n) = 8n^2 - 2n + 1.

Original entry on oeis.org

1, 7, 29, 67, 121, 191, 277, 379, 497, 631, 781, 947, 1129, 1327, 1541, 1771, 2017, 2279, 2557, 2851, 3161, 3487, 3829, 4187, 4561, 4951, 5357, 5779, 6217, 6671, 7141, 7627, 8129, 8647, 9181, 9731, 10297, 10879, 11477, 12091, 12721, 13367, 14029, 14707, 15401, 16111, 16837, 17579

Offset: 0

Paul Curtz, Feb 03 2011

Odd numbers (A005408) written clockwise as a square spiral:
.
  41--43--45--47--49--51
   |                   |
  39  13--15--17--19  53
   |   |           |   |
  37  11   1---3  21  55
   |   |       |   |   |
  35   9---7---5  23  57
   |               |   |
  33--31--29--27--25  59
                       |
  71--69--67--65--63--61
.
Walking in straight lines away from the center:
  1, 17, 49, ... = A069129(n+1) =  1 - 8*n + 8*n^2,
  1,  3, 21, ... = A033567(n)   =  1 - 6*n + 8*n^2,
  1, 15, 45, ... = A014634(n)   =  1 + 6*n + 8*n^2,
  1,  5, 25, ... = A080856(n)   =  1 - 4*n + 8*n^2,
  1, 13, 41, ... = A102083(n)   =  1 + 4*n + 8*n^2,
  1,  7, 29, ... = a(n)         =  1 - 2*n + 8*n^2,
  1, 11, 37, ... = A188135(n)   =  1 + 2*n + 8*n^2,
  1,  9, 33, ... = A081585(n)   =  1       + 8*n^2,
  5, 29, 69, ... = A108928(n+1) = -3       + 8*n^2,
  7, 31, 71, ... = A157914(n+1) = -1       + 8*n^2,
  9, 35, 77, ... = A033566(n+1) = -1 + 2*n + 8*n^2.
All are quadrisections of sequences in A181407(n) (example: A014634(n) and A033567(n) in A064038(n+1)) or of this family (?): a(n) is a quadrisection of f(n) = 1,1,1,1,2,7,11,8,11,29,37,23,28,67,79,46,... f(n) is just before A064038(n+1) (fifth vertical) in A181407(n). The companion to a(n) is A188135(n), another quadrisection of f(n). Two last quadrisections of f(n) are A054552(n) and A033951(n).
For n >= 1, bisection of A193867. - Omar E. Pol, Aug 16 2011
Also the sequence may be obtained by starting with the segment (1, 7) followed by the line from 7 in the direction 7, 29, ... in the square spiral whose vertices are the generalized hexagonal numbers (A000217). - Omar E. Pol, Aug 01 2016

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

Cf. A000217, A005408, A014634, A014635, A033566, A033567, A033951, A054552, A064038.

Cf. A069129, A080856, A081585, A102083, A108928, A157914, A181407, A188135, A193867.

[1-2*n+8*n^2: n in [0..50]]; // Vincenzo Librandi, Feb 03 2011

Table[1 - 2n + 8n^2, {n, 0, 39}] (* Alonso del Arte, Feb 03 2011 *)
CoefficientList[Series[(-1 - 4 x - 11 x^2)/(x - 1)^3, {x, 0, 47}], x] (* Michael De Vlieger, Aug 01 2016 *)

a(n)=8*n^2-2*n+1 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = a(n-1) + 16*n - 10 (n > 0).
a(n) = 2*a(n-1) - a(n-2) + 16 (n > 1).
a(n) = 3*(n-1) - 3*a(n-2) + a(n-3) (n > 2).
G.f.: (-1 - 4*x - 11*x^2)/(x-1)^3. - R. J. Mathar, Feb 03 2011
a(n) = A014635(n) + 1. - Bruno Berselli, Apr 09 2011
E.g.f.: exp(x)*(1 + 6*x + 8*x^2). - Elmo R. Oliveira, Nov 17 2024

A380472 a(n) = gcd_{primes P >= prime(n+1)} Product_{i=1..n} (P^2-i^2).

Original entry on oeis.org

1, 24, 360, 40320, 1814400, 479001600, 43589145600, 20922789888000, 3201186852864000, 2432902008176640000, 562000363888803840000, 620448401733239439360000, 201645730563302817792000000, 304888344611713860501504000000, 132626429906095529318154240000000, 263130836933693530167218012160000000

Offset: 0

Lily Bétaz, Martin Chevalier, and Basile Fusil, Jun 23 2025

a(n) is the GCD of all numbers of the form Product_{i=1..n} (P^2-i^2) where P is a prime larger than or equal to the (n+1)-th prime.

			a(1) = 24 because 24 = GCD{P^2-1^2} GCD is taken on all numbers of the form P^2-1^2 with P a prime and P>3. This implies that for all primes P>3, P^2-1 is divisible by 24.
a(2) = 360 because 360 = GCD{(P^2-1^2)(P^2-2^2)} GCD is taken on all numbers of the form (P^2-1^2)(P^2-2^2) with P a prime and P>5. This implies that for all primes P>5, (P^2-1^2)(P^2-2^2) is divisible by 360.
a(3) = 40320 because 40320 = GCD{(P^2-1^2)(P^2-2^2)(P^2-3^2)}.
b(5) = 231 = a(7)/a(6).
c(2) = 112 = a(3)/a(2).

Cf. A014634 (odd ratio), A014635 (even ratio, multiplied by 4), A084920.

seq((2*n + 2)!*(3/4 - (-1)^n/4), n = 0..20)

Table[(2*n + 2)!*(3/4 - (-1)^n/4), {n, 0, 20}]

E.g.f.: Sum_{n >= 0} a(n)/(2*n)!*z^(2*n) = (1 + 12*z^2 + 12*z^4 + 20*z^6 + 3*z^8)/(1 - z^4)^3.
a(n) = (2*n+2)!*(3/4-(-1)^n/4).
b(n) = (2*n+1)*(4*n+1) = a(2n)/a(2n-1) for n>=1 gives the odd ratios of a(n) (A014634).
c(n) = 4*2*n*(4*n-1) = a(2n-1)/a(2n-2) for n>=1 gives the even ratios of a(n) (4 times A014635).
Sum_{n>=0} 1/a(n) = 3*cosh(1)/2 - cos(1)/2 - 1. - Amiram Eldar, Jul 03 2025

A014772 Squares of even hexagonal numbers.

Original entry on oeis.org

36, 784, 4356, 14400, 36100, 76176, 142884, 246016, 396900, 608400, 894916, 1272384, 1758276, 2371600, 3132900, 4064256, 5189284, 6533136, 8122500, 9985600, 12152196, 14653584, 17522596, 20793600, 24502500, 28686736

Offset: 1

Mohammad K. Azarian

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

Cf. A014635.

Take[Table[n(2n-1),{n,60}],{2,-1,2}]^2 (* or *) LinearRecurrence[ {5,-10,10,-5,1},{36,784,4356,14400,36100},30] (* Harvey P. Dale, May 11 2012 *)

G.f.: 4*x*(9+151*x+199*x^2+25*x^3)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009

a(1)=36, a(2)=784, a(3)=4356, a(4)=14400, a(5)=36100, a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, May 11 2012

G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009

More terms from Erich Friedman

A270704 Even 14-gonal (or tetradecagonal) numbers.

Original entry on oeis.org

0, 14, 76, 186, 344, 550, 804, 1106, 1456, 1854, 2300, 2794, 3336, 3926, 4564, 5250, 5984, 6766, 7596, 8474, 9400, 10374, 11396, 12466, 13584, 14750, 15964, 17226, 18536, 19894, 21300, 22754, 24256, 25806, 27404, 29050, 30744, 32486, 34276, 36114, 38000

Offset: 0

Ilya Gutkovskiy, Mar 22 2016

First bisection of A051866.

More generally, the ordinary generating function for the even k-gonal numbers with even k or for the first bisection of k-gonal numbers, is (k*x + (3*k - 8)*x^2)/(1 - x )^3.

OEIS Wiki, Figurate numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1)

Cf. similar sequences of the even k-gonal numbers with even k: A016742 (k = 4), A014635 (k = 6), A014642 (k = 8), A028994 (k = 10), A193872 (k = 12).

LinearRecurrence[{3, -3, 1}, {0, 14, 76}, 41]
Table[2 n (12 n - 5), {n, 0, 40}]
PolygonalNumber[14,Range[0,80,2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 12 2017 *)

concat(0, Vec(2*x*(7 + 17*x)/(1 - x)^3 + O(x^60))) \\ Michel Marcus, Mar 22 2016

G.f.: 2*x*(7 + 17*x)/(1 - x)^3.
E.g.f.: 2*exp(x)*x*(7 + 12*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = 2*n*(12*n - 5).
a(n) = A005843(n)*A017605(n-1).
Sum_{n>=1} 1/a(n) = (Pi - sqrt(3)*Pi + sqrt(3)*log(27) + sqrt(3)*log(64) + log(1728) + 6*log(sqrt(3)-1) + 2*sqrt(3)*log(sqrt(3)-1) - 6*log(sqrt(3)+1) - 2*sqrt(3)*log(sqrt(3)+1))/(20 + 20*sqrt(3)) = 0.102542837854…

cp's OEIS Frontend

A139274 a(n) = n*(8*n-1).

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A134708 Even superperfect numbers divided by 2.

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A139276 a(n) = n*(8*n+3).

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A139277 a(n) = n*(8*n+5).

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A181890 a(n) = 8*n^2 + 14*n + 5.

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A153798 a(n) = A000043(n)-2.

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A185438 a(n) = 8*n^2 - 2*n + 1.

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A139274 a(n) = n(8n-1).

A139276 a(n) = n(8n+3).

A139277 a(n) = n(8n+5).

A181890 a(n) = 8n^2 + 14n + 5.

A185438 a(n) = 8n^2 - 2n + 1.