A017533 -id:A017533 - cp's OEIS frontend

A017545 a(n) = 12*n + 2.

2, 14, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 146, 158, 170, 182, 194, 206, 218, 230, 242, 254, 266, 278, 290, 302, 314, 326, 338, 350, 362, 374, 386, 398, 410, 422, 434, 446, 458, 470, 482, 494, 506, 518, 530, 542, 554, 566, 578, 590, 602, 614, 626, 638

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 40 ).

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A017533, A017557.

Subsequence of A072065.

List([0..60], n-> 2*(6*n+1) ); # G. C. Greubel, Sep 18 2019

[12*n+2: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011

A017545:=n->12*n+2: seq(A017545(n), n=0..60); # Wesley Ivan Hurt, Apr 27 2017

12*Range[0,60]+2 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

a(n)=12*n+2 \\ Charles R Greathouse IV, Jul 10 2016

[2*(6*n+1) for n in (0..60)] # G. C. Greubel, Sep 18 2019

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: 2*(1 + 5*x)/(1-x)^2.
E.g.f.: 2*(1 + 6*x)*exp(x). (End)
Sum_{n>=0} (-1)^n/a(n) = Pi/12 + sqrt(3)*log(2 + sqrt(3))/12. - Amiram Eldar, Dec 12 2021

A017569 a(n) = 12*n + 4.

Original entry on oeis.org

4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 148, 160, 172, 184, 196, 208, 220, 232, 244, 256, 268, 280, 292, 304, 316, 328, 340, 352, 364, 376, 388, 400, 412, 424, 436, 448, 460, 472, 484, 496, 508, 520, 532, 544, 556, 568, 580, 592, 604, 616, 628

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(46).
Number of 6 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1A008574; m=3: A016933; m=4: A022144; m=5: A017293. - Sergey Kitaev, Nov 13 2004
Except for 4, exponents e such that x^e - x^2 + 1 is reducible.
If Y and Z are 2-blocks of a (3n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007
Terms are perfect squares iff n is a generalized octagonal number (A001082), then n = k*(3*k-2) and a(n) = (2*(3*k-1))^2. - Bernard Schott, Feb 26 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Milan Janjic, Two Enumerative Functions.
Tanya Khovanova, Recursive Sequences.
Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 4 (2004), Article A21, 20pp.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A017533, A017545, A089911.
Cf. A016777, A016933, A017293, A022144.
Cf. A001082.

a017569 = (+ 4) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+4: n in [0..50]]; // Vincenzo Librandi, May 04 2011

12*Range[0,200]+4 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

A089911(a(n)) = 3. - Reinhard Zumkeller, Jul 05 2013
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(2)/12. - Amiram Eldar, Dec 12 2021
From Stefano Spezia, Feb 25 2023: (Start)
O.g.f.: 4*(1 + 2*x)/(1 - x)^2.
E.g.f.: 4*exp(x)*(1 + 3*x). (End)
From Elmo R. Oliveira, Apr 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2).
a(n) = 2*A016933(n) = 4*A016777(n) = A016777(4*n+1). (End)

A128470 a(n) = 30*n + 1.

Original entry on oeis.org

1, 31, 61, 91, 121, 151, 181, 211, 241, 271, 301, 331, 361, 391, 421, 451, 481, 511, 541, 571, 601, 631, 661, 691, 721, 751, 781, 811, 841, 871, 901, 931, 961, 991, 1021, 1051, 1081, 1111, 1141, 1171, 1201, 1231, 1261, 1291, 1321, 1351, 1381, 1411, 1441, 1471

Offset: 0

Cino Hilliard, May 06 2007

Possible upper bounds of twin primes pairs ending in 1: For a 30k + r "wheel", k > 0, r = 1, 13, 19 are the only possible values that can form an upper bound of a twin prime pair. The 30k+r wheel gives the sequence 1, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 49, 53, 59, ... which is frequently used in prime number sieves to skip multiples of 2, 3, 5. The fact that subtracting 2 from 30k+7, 11, 17, 23 will give us a multiple of 3 or 5 precludes these numbers from being an upper bound of a twin prime pair. This leaves us with r = 1, 13, 19 for k > 0 as the only possible cases to form an upper bound of a twin prime pair. 1, 13, 19 concludes the 6 numbers of the 8 number wheel that can form part of a twin prime pair.

			61 = 30 * 2 + 1, the upper part of the twin prime pair 59, 61.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Albert van der Horst, Counting Twin Primes
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A161700, A005408, A016813, A016921, A017281, A017533, A158057, A161705, A161709, A161714.

[30*n+1: n in [0..50]]; // Vincenzo Librandi, Jun 16 2011

Range[1, 3001, 30] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)
CoefficientList[Series[(1 + 29 x) / (1 - x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 30 2014 *)
LinearRecurrence[{2, -1}, {1, 31}, 100] (* G. C. Greubel, Apr 04 2016 *)

a(n)=30*n+1 \\ Charles R Greathouse IV, Oct 07 2015

(0 to 49).map(30 *  + 1) // _Alonso del Arte, Jun 02 2019

a(n) = 2*a(n-1) - a(n-2) for n > 1. - Vincenzo Librandi, Dec 30 2014
G.f.: (1 + 29*x)/(1 - x)^2. - Vincenzo Librandi, Dec 30 2014
E.g.f.: (1 + 30*x)*exp(x). - G. C. Greubel, Apr 04 2016

A017641 a(n) = 12*n + 10.

Original entry on oeis.org

10, 22, 34, 46, 58, 70, 82, 94, 106, 118, 130, 142, 154, 166, 178, 190, 202, 214, 226, 238, 250, 262, 274, 286, 298, 310, 322, 334, 346, 358, 370, 382, 394, 406, 418, 430, 442, 454, 466, 478, 490, 502, 514, 526, 538, 550, 562, 574, 586, 598, 610, 622, 634

Offset: 0

N. J. A. Sloane

Exponents e such that x^e + x^2 - 1 is reducible.

If Y is a 4-subset of an (2n+1)-set X then, for n>=3, a(n-2) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 16 2007

Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016969, A017533, A017545, A017593, A030132.

Range[10, 1000, 12] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)

a(n)=12*n+10 \\ Charles R Greathouse IV, Jul 10 2016

A030132(a(n)) = 9. - Reinhard Zumkeller, Jul 04 2007
G.f.: 2*(5 + x)/(1 - x)^2. - Stefano Spezia, May 09 2021
Sum_{n>=0} (-1)^n/a(n) = Pi/12 - sqrt(3)*log(2 + sqrt(3))/12. - Amiram Eldar, Dec 12 2021
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: 2*exp(x)*(5 + 6*x).
a(n) = 2*A016969(n).
a(n) = 2*a(n-1) - a(n-2) for n >= 2. (End)

A287326 Triangle read by rows: T(n, k) = 6k(n-k) + 1; n >= 0, 0 <= k <= n.

Original entry on oeis.org

1, 1, 1, 1, 7, 1, 1, 13, 13, 1, 1, 19, 25, 19, 1, 1, 25, 37, 37, 25, 1, 1, 31, 49, 55, 49, 31, 1, 1, 37, 61, 73, 73, 61, 37, 1, 1, 43, 73, 91, 97, 91, 73, 43, 1, 1, 49, 85, 109, 121, 121, 109, 85, 49, 1, 1, 55, 97, 127, 145, 151, 145, 127, 97, 55, 1, 1, 61, 109, 145, 169, 181, 181, 169, 145, 109, 61, 1

Offset: 0

Kolosov Petro, Aug 31 2017

From Kolosov Petro, Apr 12 2020: (Start)
Let A(m, r) = A302971(m, r) / A304042(m, r).
Let L(m, n, k) = Sum_{r=0..m} A(m, r) * k^r * (n - k)^r.
Then T(n, k) = L(1, n, k), i.e T(n, k) is partial case of L(m, n, k) for m = 1.
T(n, k) is symmetric: T(n, k) = T(n, n-k). (End)

			Triangle begins:
  ----------------------------------------
  k=    0   1   2   3   4   5   6   7   8
  ----------------------------------------
  n=0:  1;
  n=1:  1,  1;
  n=2:  1,  7,  1;
  n=3:  1, 13, 13,  1;
  n=4:  1, 19, 25, 19,  1;
  n=5:  1, 25, 37, 37, 25,  1;
  n=6:  1, 31, 49, 55, 49, 31,  1;
  n=7:  1, 37, 61, 73, 73, 61, 37,  1;
  n=8:  1, 43, 73, 91, 97, 91, 73, 43,  1;

Georg Fischer, Table of n, a(n) for n = 0..495 [rows 0..10 and 12..30 from Kolosov Petro]
Petro Kolosov, On the link between binomial theorem and discrete convolution, arXiv:1603.02468 [math.NT], 2016-2025.
Petro Kolosov, Polynomial identity involving binomial theorem and Faulhaber's formula, 2023.
Petro Kolosov, History and overview of the polynomial P_b^m(x), 2024.

Columns k=0..6 give A000012, A016921, A017533, A161705, A103214, A128470, A158065.
Column sums k=0..4 give A000027, A000567, A051866, A051872, A255185.
Row sums give A001093.
Various cases of L(m, n, k): This sequence (m=1), A300656(m=2), A300785(m=3). See comments for L(m, n, k).
Differences of cubes n^3 are T(A000124(n), 1).
Cf. A000124, A000578, A003154, A003215, A007318, A008458, A016969.
Cf. A038593, A055012, A068601, A077028, A094053, A166873, A227776.
Cf. A294317, A302971, A304042.

Flat(List([0..11],n->List([0..n],k->6*k*(n-k)+1))); # Muniru A Asiru, Oct 09 2018

/* As triangle */ [[6*k*(n-k) + 1: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Oct 26 2018

T := (n, k) -> 6*k*(n-k) + 1:
seq(seq(T(n, k), k=0..n), n=0..11); # Muniru A Asiru, Oct 09 2018

T[n_, k_] := 6 k (n - k) + 1; Column[Table[T[n, k], {n, 0, 10}, {k, 0, n}], Center] (* Kolosov Petro, Jun 02 2019 *)

t(n, k) = 6*k*(n-k)+1
trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print(""))
/* Print initial 9 rows of triangle as follows */
trianglerows(9) \\ Felix Fröhlich, Jan 09 2018

def A287326(n,k): return 6*k*(n-k) + 1
flatten([[A287326(n,k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Sep 25 2024

T(n, k) = 6*k*(n-k) + 1.
G.f. of column k: n^k*(1+(6*k-1)*n)/(1-n)^2.
G.f.: (1 - x - x*y + 7*x^2*y)/((1 - x)^2*(1 - x*y)^2). - Stefano Spezia, Oct 09 2018 [Adapted by Stefano Spezia, Sep 25 2024]
From Kolosov Petro, Jun 05 2019: (Start)
T(n, k) = 1/2 * T(A294317(n, k), k) + 1/2.
T(n+1, k) = 2*T(n, k) - T(n-1, k), for n >= k.
T(n, k) = 6*A077028(n, k) - 5.
T(2n, n) = A227776(n).
T(2n+1, n) = A003154(n+1).
T(2n+3, n) = A166873(n+1).
Sum_{k=0..n-1} T(n, k) = Sum_{k=1..n} T(n, k) = A000578(n).
Sum_{k=1..n-1} T(n, k) = A068601(n).
(n+1)^3 - n^3 = T(A000124(n), 1). (End)
Sum_{k=0..n} (-1)^k*T(n, k) = (-1/2)*(1 + (-1)^n)*A016969(floor(n/2) - 1). - G. C. Greubel, Sep 25 2024

A017605 a(n) = 12*n + 7.

Original entry on oeis.org

7, 19, 31, 43, 55, 67, 79, 91, 103, 115, 127, 139, 151, 163, 175, 187, 199, 211, 223, 235, 247, 259, 271, 283, 295, 307, 319, 331, 343, 355, 367, 379, 391, 403, 415, 427, 439, 451, 463, 475, 487, 499, 511, 523, 535, 547, 559, 571, 583, 595, 607, 619, 631

Offset: 0

N. J. A. Sloane

Tanya Khovanova, Recursive Sequences
Leo Tavares, Illustration: Hexagonal Wheels
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016921, A017533, A017545, A068229.

Cf. A000217, A003215, A049453, A142241.

12*Range[0,200] + 7 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

a(n)=12*n+7 \\ Charles R Greathouse IV, Jul 10 2016

[i+7 for i in range(525) if gcd(i,12) == 12] # Zerinvary Lajos, May 21 2009

a(n) = 2*(12*n+1) - a(n-1) = 2*a(n-1) - a(n-2) with a(0) = 7, a(1) = 19. - Vincenzo Librandi, Nov 19 2010
a(n) = (n+1)*A016921(n+1) - n*A016921(n). - Bruno Berselli, Jan 18 2013
a(n) = A003215(n+1) - 6*A000217(n-1). - Leo Tavares, Jul 25 2021
From Elmo R. Oliveira, Apr 02 2024: (Start)
G.f.: (7+5*x)/(1-x)^2.
E.g.f.: exp(x)*(7 + 12*x).
a(n) = A049453(n+1) - A049453(n) = A142241(n)/2. (End)

A017617 a(n) = 12*n + 8.

Original entry on oeis.org

8, 20, 32, 44, 56, 68, 80, 92, 104, 116, 128, 140, 152, 164, 176, 188, 200, 212, 224, 236, 248, 260, 272, 284, 296, 308, 320, 332, 344, 356, 368, 380, 392, 404, 416, 428, 440, 452, 464, 476, 488, 500, 512, 524, 536, 548, 560, 572, 584, 596, 608, 620, 632, 644, 656

Offset: 0

N. J. A. Sloane

Also the number of cube units that frame a cube of edge length n+1. - Peter M. Chema, Mar 27 2016

			For n=3; a(3)= 12*3 + 8 = 44.
Thus, there are 44 cube units that frame a cube of edge length 4. - _Peter M. Chema_, Mar 26 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016789, A016933, A016957, A017533, A017545, A089911.

a017617 = (+ 8) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+8: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

12*Range[0,200]+8 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

my(x='x+O('x^99)); Vec(4*(2+x)/(1-x)^2) \\ Altug Alkan, Mar 27 2016

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 08 2011
A089911(a(n)) = 9. - Reinhard Zumkeller, Jul 05 2013
G.f.: 12*x/(1-x)^2 + 8/(1-x) = 4*(2+x)/(1-x)^2. (see the PARI program). - Wolfdieter Lang, Oct 11 2021
Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 - log(2)/12. - Amiram Eldar, Dec 12 2021
From Elmo R. Oliveira, Apr 04 2025: (Start)
E.g.f.: 4*exp(x)*(2 + 3*x).
a(n) = 4*A016789(n) = 2*A016957(n) = A016933(2*n+1). (End)

A017557 a(n) = 12*n + 3.

Original entry on oeis.org

3, 15, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 147, 159, 171, 183, 195, 207, 219, 231, 243, 255, 267, 279, 291, 303, 315, 327, 339, 351, 363, 375, 387, 399, 411, 423, 435, 447, 459, 471, 483, 495, 507, 519, 531, 543, 555, 567, 579, 591, 603, 615, 627, 639

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 44 ).

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016813, A017533, A017545, A089911.

List([0..60], n-> 12*n+3 ); # G. C. Greubel, Sep 18 2019

a017557 = (+ 3) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+3: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011

seq(12*n+3, n=0..60); # G. C. Greubel, Sep 18 2019

12*Range[0,60]+3 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

a(n)=12*n+3 \\ Charles R Greathouse IV, Jul 10 2016

[12*n+3 for n in (0..60)] # G. C. Greubel, Sep 18 2019

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011
A089911(2*a(n)) = 8. - Reinhard Zumkeller, Jul 05 2013
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: 3*(1+3*x)/(1-x)^2.
E.g.f.: 3*(1+4*x)*exp(x). (End)
Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(sqrt(2)+1))/(12*sqrt(2)). - Amiram Eldar, Dec 12 2021

A017653 a(n) = 12*n + 11.

Original entry on oeis.org

11, 23, 35, 47, 59, 71, 83, 95, 107, 119, 131, 143, 155, 167, 179, 191, 203, 215, 227, 239, 251, 263, 275, 287, 299, 311, 323, 335, 347, 359, 371, 383, 395, 407, 419, 431, 443, 455, 467, 479, 491, 503, 515, 527, 539, 551, 563, 575, 587, 599, 611, 623, 635

Offset: 0

N. J. A. Sloane

Or, with a different offset, 12*n - 1. In any case, numbers congruent to -1 (mod 12). - Alonso del Arte, May 29 2011

Numbers congruent to 2 (mod 3) and 3 (mod 4). - Bruno Berselli, Jul 06 2017

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
John Elias, 60*n+55 Triangular Snowflakes.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1000.
Tanya Khovanova, Recursive Sequences.
Leo Tavares, Illustration: Twin Hexagonal Frames.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A003215, A008594, A016969, A017533, A017545, A089911.

Subsequence of A072065.

a017653 = (+ 11) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+11: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

Array[12*#+11&,100,0] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)

PARI
```
a(n)=12*n+11
```

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 08 2011
G.f.: (11+x)/(1-x)^2. - Colin Barker, Feb 19 2012
A089911(2*a(n)) = 11. - Reinhard Zumkeller, Jul 05 2013
a(n) = 2*A003215(n+1) - 1 - 2*A003215(n). See Twin Hexagonal Frames illustration. - Leo Tavares, Aug 19 2021
From Elmo R. Oliveira, Apr 12 2025: (Start)
E.g.f.: exp(x)*(11 +  12*x).
a(n) = A016969(2*n+1). (End)

A017581 a(n) = 12*n + 5.

Original entry on oeis.org

5, 17, 29, 41, 53, 65, 77, 89, 101, 113, 125, 137, 149, 161, 173, 185, 197, 209, 221, 233, 245, 257, 269, 281, 293, 305, 317, 329, 341, 353, 365, 377, 389, 401, 413, 425, 437, 449, 461, 473, 485, 497, 509, 521, 533, 545, 557, 569, 581, 593, 605, 617, 629

Offset: 0

N. J. A. Sloane

Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0(71).
A089911(2*a(n)) = 7. - Reinhard Zumkeller, Jul 05 2013
Equivalently, intersection of A016813 and A016789. - Bruno Berselli, Jan 24 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008594, A016789, A016813, A016969, A017533, A017545, A017593, A089911.

a017581 = (+ 5) . (* 12)  -- Reinhard Zumkeller, Jul 05 2013

[12*n+5: n in [0..60]]; // Vincenzo Librandi, Jun 08 2011

12*Range[0,200]+5 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)

a(n)=12*n+5 \\ Charles R Greathouse IV, Jul 10 2016

a(n) = 2*a(n-1) - a(n-2) for n>1, a(0)=5, a(1)=17. - Vincenzo Librandi, Jun 08 2011
G.f.: x*(5 + 7*x)/(1 - x)^2. - Wolfdieter Lang, Jul 04 2023
E.g.f.: exp(x)*(5 + 12*x). - Stefano Spezia, Feb 21 2024
a(n) = A016969(2*n) = A016789(4*n+1). - Elmo R. Oliveira, Apr 10 2025

cp's OEIS Frontend

A017545 a(n) = 12*n + 2.

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A017569 a(n) = 12*n + 4.

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A128470 a(n) = 30*n + 1.

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A017641 a(n) = 12*n + 10.

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A287326 Triangle read by rows: T(n, k) = 6*k*(n-k) + 1; n >= 0, 0 <= k <= n.

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A017605 a(n) = 12*n + 7.

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Sage

Formula

A287326 Triangle read by rows: T(n, k) = 6k(n-k) + 1; n >= 0, 0 <= k <= n.