A060544 -id:A060544 - cp's OEIS frontend

A001504 a(n) = (3n+1)(3*n+2).

2, 20, 56, 110, 182, 272, 380, 506, 650, 812, 992, 1190, 1406, 1640, 1892, 2162, 2450, 2756, 3080, 3422, 3782, 4160, 4556, 4970, 5402, 5852, 6320, 6806, 7310, 7832, 8372, 8930, 9506, 10100, 10712, 11342, 11990, 12656, 13340, 14042, 14762, 15500, 16256, 17030

Offset: 0

N. J. A. Sloane

The oblong numbers (A002378) not divisible by 3. - Gionata Neri, May 10 2015

The continued fraction expansion of sqrt(a(n)+1) is [3n+1; {1, 1, 2n, 1, 1,6n+2}]. For n=0, this collapses to [1; {1, 2}]. - Magus K. Chu, Nov 13 2024

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

Subsequence of A002378.

Cf. A016777, A016789, A060544, A073010, A387235.

A001504:=n->(3*n+1)*(3*n+2): seq(A001504(n), n=0..100); # Wesley Ivan Hurt, Jan 29 2017

Table[(3*n+1)*(3*n+2),{n,50}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
LinearRecurrence[{3,-3,1},{2,20,56},80] (* Harvey P. Dale, Mar 16 2025 *)

a(n)=(3*n+1)*(3*n+2) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = A060544(n+1)*2.
Sum_{k>=0} 1/a(k) = (Pi/3)/sqrt(3) = A073010. - Benoit Cloitre, Aug 20 2002
a(n) = 18*n + a(n-1) with a(0) = 2. - Vincenzo Librandi, Nov 12 2010
Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/3 (A387235). - Amiram Eldar, Jan 14 2021
G.f.: -2*(x^2+7*x+1)/(x-1)^3. - Alois P. Heinz, Feb 28 2021
From Amiram Eldar, Feb 19 2023: (Start)
a(n) = A016777(n)*A016789(n).
Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6)/sqrt(3).
Product_{n>=0} (1 + 1/a(n)) = 2*cosh(sqrt(3)*Pi/6)/sqrt(3). (End)
E.g.f.: exp(x)*(2 + 18*x + 9*x^2). - Stefano Spezia, Aug 23 2025

A190152 Triangle of binomial coefficients binomial(3n-k,3n-3*k).

Original entry on oeis.org

1, 1, 1, 1, 10, 1, 1, 28, 35, 1, 1, 55, 210, 84, 1, 1, 91, 715, 924, 165, 1, 1, 136, 1820, 5005, 3003, 286, 1, 1, 190, 3876, 18564, 24310, 8008, 455, 1, 1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1, 1, 325, 12650, 134596, 490314, 646646, 293930, 38760, 969, 1

Offset: 0

Emanuele Munarini, May 05 2011

From R. J. Mathar, Mar 15 2013: (Start)
The matrix inverse starts
  1;
  -1,1;
  9,-10,1;
  -288,322,-35,1;
  22356,-25003,2730,-84,1;
  -3428973,3835026,-418825,12936,-165,1;
  914976405,-1023326973,111759115,-3452449,44187,-286,1;
  ... (End)

			Triangle begins:
  1
  1, 1
  1, 10, 1
  1, 28, 35, 1
  1, 55, 210, 84, 1
  1, 91, 715, 924, 165, 1
  1, 136, 1820, 5005, 3003, 286, 1
  1, 190, 3876, 18564, 24310, 8008, 455, 1
  1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1
  ...

Nathaniel Johnston, Rows n = 0..100, flattened

Cf. A000447 (first subdiagonal), A053135 (second subdiagonal), A060544 (second column), A190088, A190153 (row sums), A190154 (diagonal sums).

Flatten[Table[Binomial[3n - k, 3n - 3k], {n, 0, 9}, {k, 0, n}]]

create_list(binomial(3*n-k,3*n-3*k),n,0,9,k,0,n);

for(n=0,10, for(k=0,n, print1(binomial(3*n-k, 3*(n-k)), ", "))) \\ G. C. Greubel, Dec 29 2017

A048909 9-gonal (or nonagonal) triangular numbers.

Original entry on oeis.org

1, 325, 82621, 20985481, 5330229625, 1353857339341, 343874433963061, 87342752369278225, 22184715227362706161, 5634830324997758086741, 1431224717834203191326125, 363525443499562612838749081, 92334031424171069457850940521, 23452480456295952079681300143325

Offset: 1

Eric W. Weisstein

We want solutions to m(7m-5)/2 = n(n+1)/2, or equivalently (14m-5)^2 = 7(2n+1)^2 + 18. This is the Pell-type equation x^2 - 7y^2 = 18.
This equation has unit solutions (x,y) = (5,1), (9, 3) and (19, 7), which lead to the family of solutions (5, 1), (9, 3), (19, 7), (61, 23), (135, 51), (299, 113), (971, 367), .... The corresponding integer solutions are (m,n) = (1,1), (10, 25), (154, 406), (2449, 6478), ... (A048907 and A048908), giving the nonagonal triangular numbers 1, 325, 82621, 20985481, ... shown here.
Also, numbers simultaneously 9-gonal and centered 9-gonal, the intersection of A001106 and A060544. - Steven Schlicker, Apr 24 2007

Colin Barker, Table of n, a(n) for n = 1..416
S. C. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, Mathematics Magazine, Vol. 84, No. 5, December 2011, pp. 339-350.
Eric Weisstein's World of Mathematics, Nonagonal Triangular Number.
Index entries for linear recurrences with constant coefficients, signature (255,-255,1).

Cf. A001106, A060544, A048907, A048908.

CP := n -> 1+1/2*9*(n^2-n): N:=10: u:=8: v:=1: x:=9: y:=1: k_pcp:=[1]: for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+63*tempy*v: y:=tempx*v+tempy*u: s:=(y+1)/2: k_pcp:=[op(k_pcp),CP(s)]: end do: k_pcp; # Steven Schlicker, Apr 24 2007

LinearRecurrence[{255, -255, 1}, {1, 325, 82621}, 12]; (* Ant King, Nov 03 2011 *)

Vec(-x*(x^2+70*x+1)/((x-1)*(x^2-254*x+1)) + O(x^20)) \\ Colin Barker, Jun 22 2015

Define x(n) + y(n)*sqrt(63) = (9+sqrt(63))*(8+sqrt(63))^n, s(n) = (y(n)+1)/2; then a(n) = (2+9*(s(n)^2-s(n)))/2. - Steven Schlicker, Apr 24 2007
a(n+1) = 254*a(n+1)-a(n)+72. - Richard Choulet, Sep 22 2007
a(n+1) = 127*a(n+1)+36+6*(448*a(n)^2+256*a(n)+25)^0.5. - Richard Choulet, Sep 22 2007
G.f.: z*(1+70*z+z^2)/((1-z)*(1-254*z+z^2)). - Richard Choulet, Sep 22 2007
From Ant King, Nov 03 2011: (Start)
a(n) = 255*a(n-1) - 255*a(n-2) + a(n-3).
a(n) = 1/112*(9*(8 + 3*sqrt(7))^(2n-1) + 9*(8-3* sqrt(7))^(2n-1) - 32).
a(n) = floor(9/112*(8 + 3*sqrt(7))^(2n-1)).
Limit_{n -> oo} a(n)/a(n-1) = (8 + 3*sqrt(7))^2. (End)

Edited by N. J. A. Sloane at the suggestion of Richard Choulet, Sep 22 2007

A081272 Downward vertical of triangular spiral in A051682.

Original entry on oeis.org

1, 25, 85, 181, 313, 481, 685, 925, 1201, 1513, 1861, 2245, 2665, 3121, 3613, 4141, 4705, 5305, 5941, 6613, 7321, 8065, 8845, 9661, 10513, 11401, 12325, 13285, 14281, 15313, 16381, 17485, 18625, 19801, 21013, 22261, 23545, 24865, 26221, 27613, 29041, 30505

Offset: 0

Paul Barry, Mar 15 2003

Reflection of A081271 in the horizontal A051682.
Binomial transform of (1, 24, 36, 0, 0, 0, .....).
One of the six verticals of a triangular spiral which starts with 1 (see the link). Other verticals are A060544, A081589, A080855, A157889, A038764. - Yuriy Sibirmovsky, Sep 18 2016.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Kaie Kubjas, Luca Sodomaco, and Elias Tsigaridas, Exact solutions in low-rank approximation with zeros, arXiv:2010.15636 [math.AG], 2020.
Yuriy Sibirmovsky, Six verticals of the triangular spiral.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A051682.

Cf. A062741, A060544, A081589, A080855, A157889, A038764.

Table[n^2 + (n + 1)^2, {n, 0, 300, 3}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 25, 85}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2012 *)
Table[n^2 + (n + 1)^2, {n, 0, 150, 3}] (* Vincenzo Librandi, Aug 07 2013 *)

x='x+O('x^99); Vec((1+22*x+13*x^2)/(1-x)^3) \\ Altug Alkan, Sep 18 2016

a(n) = C(n, 0) + 24*C(n, 1) + 36*C(n, 2).
a(n) = 18*n^2 + 6*n + 1.
G.f.: (1 + 22*x + 13*x^2)/(1 - x)^3.
E.g.f.: exp(x)*(1 + 24*x + 18*x^2). - Stefano Spezia, Mar 07 2023

A082286 a(n) = 18*n + 10.

Original entry on oeis.org

10, 28, 46, 64, 82, 100, 118, 136, 154, 172, 190, 208, 226, 244, 262, 280, 298, 316, 334, 352, 370, 388, 406, 424, 442, 460, 478, 496, 514, 532, 550, 568, 586, 604, 622, 640, 658, 676, 694, 712, 730, 748, 766, 784, 802, 820, 838, 856, 874, 892, 910, 928, 946

Offset: 0

Cino Hilliard, May 10 2003

Solutions to (11^x + 13^x) mod 19 = 17.

Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Tanya Khovanova, Recursive Sequences
Leo Tavares, Illustration: Triangles
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A006370, A008600, A016945, A161705.

Cf. A000217, A017221, A022267, A060544.

[18*n + 10: n in [0..60]]; // Vincenzo Librandi, May 05 2011

Range[10, 1000, 18] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)

a(n)=18*n+10 \\ Charles R Greathouse IV, Jul 10 2016

a(n) = A006370(A016945(n)). - Reinhard Zumkeller, Apr 17 2008
a(n) = 2*A017221(n). - Michel Marcus, Feb 15 2014
a(n) = A060544(n+2) - 9*A000217(n-1). - Leo Tavares, Oct 15 2022
From Elmo R. Oliveira, Apr 08 2024: (Start)
G.f.: 2*(5+4*x)/(1-x)^2.
E.g.f.: 2*exp(x)*(5 + 9*x).
a(n) = 2*a(n-1) - a(n-2) for n >= 2.
a(n) = 2*(A022267(n+1) - A022267(n)). (End)

More terms from Reinhard Zumkeller, Apr 17 2008

A158623 Denominator of the reduced fraction A158620(n)/A158621(n).

Original entry on oeis.org

9, 18, 10, 45, 63, 28, 108, 135, 55, 198, 234, 91, 315, 360, 136, 459, 513, 190, 630, 693, 253, 828, 900, 325, 1053, 1134, 406, 1305, 1395, 496, 1584, 1683, 595, 1890, 1998, 703, 2223, 2340, 820, 2583, 2709, 946, 2970, 3105, 1081, 3384, 3528, 1225, 3825

Offset: 2

Jonathan Vos Post, Mar 23 2009

A158620(n) = Product_{k=2..n} (k^3-1). A158621(n) = Product_{k=2..n} (k^3+1). A158622(n) is the numerator of the reduced fraction A158620(n)/A158621(n). A158623(n) is the denominator of the reduced fraction A158620(n)/A158621(n). The reduced fractions are 7/9, 13/18, 7/10, 31/45, 43/63, 19/28, 73/108, 91/135, 37/55, 133/198, ...

			a(2) = 9 = denominator of (2^3-1)/2^3+1 = 7/9. a(3) = 18 = denominator of ((2^3-1)*(3^3-1))/((2^3+1)*(3^3+1)) = (7 * 26)/ (9 * 28) = 182/252 = 13/18. a(4) = 10 = denominator of ((2^3-1)*(3^3-1)*(4^3-1))/((2^3+1)*(3^3+1)*(4^3+1)) = (7 * 26 * 63)/(9 * 28 * 65) = 11466/16380 = 7/10. a(5) = 45 = denominator of ((2^3-1)(3^3-1)(4^3-1)(5^3-1))/((2^3+1)(3^3+1)(4^3+1)(5^3+1)) = 1421784/2063880 = 31/45.

Cf. A001093, A016921, A068601, A158620-A158622.

A158623 := proc(n) 2*(n^2+n+1)/3/n/(n+1) ; denom(%) ; end: seq(A158623(n),n=2..100) ; # R. J. Mathar, Mar 27 2009

Denominator of (Product_{k=2..n} (k^3-1)) / Product_{k=2..n} (k^3+1) = denominator of Product_{k=2..n} A068601(k)/A001093(k).
A158620(n)/A158621(n) = 2(n^2+n+1)/(3n(n+1)). Conjecture: a(n) = 3a(n-3) - 3a(n-6) + a(n-9), so trisections are A152996, A060544 and 3*A081266. - R. J. Mathar, Mar 27 2009
Empirical g.f.: -x^2*(x^8 - 2*x^5 + 9*x^4 + 18*x^3 + 10*x^2 + 18*x + 9) / ((x-1)^3*(x^2 + x + 1)^3). - Colin Barker, May 09 2013

More terms from R. J. Mathar, Mar 27 2009

A194767 Denominator of the fourth increasing diagonal of the autosequence of second kind from (-1)^n / (n+1).

Original entry on oeis.org

2, 2, 12, 20, 10, 42, 56, 24, 90, 110, 44, 156, 182, 70, 240, 272, 102, 342, 380, 140, 462, 506, 184, 600, 650, 234, 756, 812, 290, 930, 992, 352, 1122, 1190, 420, 1332, 1406, 494, 1560, 1640, 574, 1806, 1892, 660, 2070, 2162, 752, 2352, 2450, 850, 2652, 2756, 954, 2970, 3080, 1064, 3306, 3422, 1180, 3660

Offset: 0

Paul Curtz, Sep 02 2011

The autosequence of first kind from (-1)^n/(n+1) is A189733.
For the second kind (the second increasing diagonal is (-1)^n/(n+1), half of the main one):
      2,     1,     0,  -1/2,  -1/3,   1/6,   1/2,  5/12,
     -1,    -1,  -1/2,   1/6,   1/2,   1/3, -1/12, -7/20,
      0,   1/2,   2/3,   1/3,  -1/6, -5/12, -4/15,  1/12,
    1/2,   1/6,  -1/3,  -1/2,  -1/4,  3/20,  7/20, 13/60,
   -1/3,  -1/2,  -1/6,   1/4,   2/5,   1/5, -2/15, -3/10,
   -1/6,   1/3,  5/12,  3/20,  -1/5,  -1/3,  -1/6,  5/42,
    1/2,  1/12, -4/15, -7/20, -2/15,   1/6,   2/7,   1/7,
  -5/12, -7/20, -1/12, 13/60,  3/10,  5/42,  -1/7,  -1/4.
Main diagonal: (period 2:repeat 2, -1)/A026741(n+1).
Second (increasing) diagonal: (-1)^n / (n+1).
Third (increasing) diagonal: (-1)^(n+1)*A026741(n) / A045896(n).
Fourth (increasing) diagonal: (-1)^(n+1)*A146535(n)/ a(n).

OEIS Wiki, Autosequence.
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Cf. A001504 = 2*A060544, A049450 = 2*A000326, A045945 = 6*A005449.

Cf. A026741, A045896, A051176, A146535, A189733, A306368.

c = Table[1/9 (7 n + 7 n^2 + 2 n Cos[2 n *Pi/3] + 2 n^2 Cos[2 n *Pi/3] + 2 Sqrt[3] n Sin[2 n *Pi/3] + 2 Sqrt[3] n^2 Sin[2 n *Pi/3]), {n, 1, 50}] (* Roger Bagula, Mar 25 2012 *)
a[n_] := (n+1) * Numerator[(n+2)/3]; Array[a, 60, 0] (* Amiram Eldar, Sep 17 2023 *)
LinearRecurrence[{0,0,3,0,0,-3,0,0,1},{2,2,12,20,10,42,56,24,90},60] (* Harvey P. Dale, May 15 2025 *)

a(3*n) = (3*n+1)*(3*n+2), a(3*n+1) = (n+1)*(3*n+2), a(3*n+2) = 3*(n+1)*(3*n+4).
G.f.: 2*(1+x+6*x^2+7*x^3+2*x^4+3*x^5+x^6)/(1-x^3)^3. - Jean-François Alcover, Nov 11 2016
a(n+2) = 2 * A306368(n) for n >= 0. - Joerg Arndt, Aug 25 2023
a(n) = (n+1) * A051176(n+2) for n >= 0. - Paul Curtz, Sep 13 2023
Sum_{n>=0} 1/a(n) = 1 + log(3) - Pi/(3*sqrt(3)). - Amiram Eldar, Sep 17 2023

A285812 Primes equal to a centered 9-gonal number plus 1.

Original entry on oeis.org

2, 11, 29, 137, 191, 821, 947, 2081, 2927, 3917, 5051, 6329, 11027, 13367, 14879, 15401, 17021, 17579, 21737, 22367, 24977, 36857, 39341, 43661, 47279, 50087, 58997, 62129, 66431, 70877, 95267, 96581, 106031, 113051, 117371, 129287, 130817, 135461, 156521

Offset: 1

Colin Barker, Apr 27 2017

nonn

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A000040, A060544, A285809, A285810, A285811.

cpg(m, n) = m*n*(n-1)/2+1 \\ n-th centered m-gonal number
maxk=600; L=List(); for(k=1, maxk, if(isprime(p=cpg(9, k) + 1), listput(L, p))); Vec(L)

A306368 a(n) = numerator of (n + 3)(n + 4)/((n + 1)(n + 2)).

Original entry on oeis.org

6, 10, 5, 21, 28, 12, 45, 55, 22, 78, 91, 35, 120, 136, 51, 171, 190, 70, 231, 253, 92, 300, 325, 117, 378, 406, 145, 465, 496, 176, 561, 595, 210, 666, 703, 247, 780, 820, 287, 903, 946, 330, 1035, 1081, 376, 1176, 1225, 425, 1326, 1378, 477, 1485, 1540, 532, 1653, 1711, 590

Offset: 0

Peter Bala, Feb 14 2019

If P(x) and Q(x) are coprime integral polynomials such that Q(n) > 0 for n >= 0 then the sequence of numerators of the rational numbers P(n)/Q(n) for n >= 0 and the sequence of denominators of P(n)/Q(n) for n >= 0 are both quasi-polynomial in n. In fact, there exists a purely periodic sequence b(n) such that numerator(P(n)/Q(n)) = P(n)/b(n) and denominator(P(n)/Q(n)) = Q(n)/b(n). Here we take P(n) = (n + 3)*(n + 4) and Q(n) = (n + 1)*(n + 2).

Muniru A Asiru, Table of n, a(n) for n = 0..10000
Peter Bala, A note on the sequence of numerators of a rational function .
Wikipedia, Quasi-polynomial.
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Cf. A000326, A060544, A081266, A306367.

List([0..100],n->NumeratorRat((n+3)*(n+4)/((n+1)*(n+2)))); # Muniru A Asiru, Feb 25 2019

seq((n + 3)*(n + 4)/gcd((n + 3)*(n + 4), (n + 1)*(n + 2)), n = 0..100);

Table[((n+3)(n+4))/((n+1)(n+2)),{n,0,60}]//Numerator (* or *) LinearRecurrence[{0,0,3,0,0,-3,0,0,1},{6,10,5,21,28,12,45,55,22},60] (* Harvey P. Dale, Mar 28 2020 *)

a(n) = numerator((n + 3)*(n + 4)/((n + 1)*(n + 2))); \\ Michel Marcus, Feb 26 2019

O.g.f.: (x^8 + x^7 - 3*x^5 - 2*x^4 + 3*x^3 + 5*x^2 + 10*x + 6)/((1 - x)^3*(x^2 + x + 1)^3).
a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n >= 9.
a(n) = (n + 3)*(n + 4)/b(n), where (b(n))n>=0 is the purely periodic sequence [2, 2, 6, 2, 2, 6, ...] with period 3.
a(n) = (n + 3)*(n + 4)/gcd((n + 3)*(n + 4), (n + 1)*(n + 2)).
a(3*n)   = (3*n + 3)*(3*n + 4)/2 = A081266(n+1).
a(3*n+1) = (3*n + 4)*(3*n + 5)/2 = A060544(n+2).
a(3*n+2) = (n + 2)*(3*n + 5)/2   = A000326(n+2).
Sum_{n>=0} 1/a(n) = 2*log(3) - 2*Pi/(3*sqrt(3)). - Amiram Eldar, Aug 11 2022

A027626 Denominator of n(n+5)/((n+2)(n+3)).

Original entry on oeis.org

1, 2, 10, 5, 7, 28, 12, 15, 55, 22, 26, 91, 35, 40, 136, 51, 57, 190, 70, 77, 253, 92, 100, 325, 117, 126, 406, 145, 155, 496, 176, 187, 595, 210, 222, 703, 247, 260, 820, 287, 301, 946, 330, 345, 1081, 376, 392, 1225, 425, 442, 1378, 477, 495, 1540, 532, 551

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Peter Bala, A note on the sequence of numerators of a rational function, 2019.
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Cf. A000292, A027625, A061347, A107711, A234041.

[Denominator(n*(n+5)/((n+2)*(n+3))): n in [0..60]]; // Vincenzo Librandi, Mar 04 2014

CoefficientList[Series[(1+2*x+10*x^2+2*x^3+x^4-2*x^5+x^8)/(1-x^3)^3, {x,0,50}], x] (* Vincenzo Librandi, Mar 04 2014 *)

a(n) = numerator((n+2)*(n+3)/6); \\ Altug Alkan, Apr 18 2018

[numerator(binomial(n+3,2)/3) for n in (0..60)] # G. C. Greubel, Aug 04 2022

a(n) = GCD of n-th and (n+1)st tetrahedral numbers (A000292). - Ross La Haye, Sep 13 2003
G.f.: (1 +2*x +10*x^2 +2*x^3 +x^4 -2*x^5 +x^8)/(1-x^3)^3.
a(n) = A234041(n+1) = A107711(n+4,3) = C(n+3,2)*gcd(n+4,3)/3 for n >= 0. See the o.g.f. of A234041. - Wolfdieter Lang, Feb 26 2014
a(n) = numerator of (n+2)*(n+3)/6. - Altug Alkan, Apr 18 2018
Sum_{n>=0} 1/a(n) = 5 - 4*Pi/(3*sqrt(3)). - Amiram Eldar, Aug 11 2022
a(n) = (n + 2)*(n + 3)*(5 - 2*A061347(n+1))/18. - Stefano Spezia, Oct 16 2023
a(n) is quasi-polynomial in n: a(3*n) = (n+1)*(3*n+2)/2 = A000326(n+1); a(3*n+1) = (n+1)*(3*n+4)/2 = A005449(n+1); a(3*n+2) = (3*n+4)*(3*n+5)/2 = A060544(n+2). - Peter Bala, Nov 20 2024

More terms from Vincenzo Librandi, Mar 04 2014

cp's OEIS Frontend

A001504 a(n) = (3*n+1)*(3*n+2).

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A190152 Triangle of binomial coefficients binomial(3*n-k,3*n-3*k).

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Maxima

PARI

A048909 9-gonal (or nonagonal) triangular numbers.

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Maple

Mathematica

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A081272 Downward vertical of triangular spiral in A051682.

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A082286 a(n) = 18*n + 10.

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Magma

Mathematica

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A158623 Denominator of the reduced fraction A158620(n)/A158621(n).

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Maple

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A194767 Denominator of the fourth increasing diagonal of the autosequence of second kind from (-1)^n / (n+1).

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A001504 a(n) = (3n+1)(3*n+2).

A190152 Triangle of binomial coefficients binomial(3n-k,3n-3*k).

A306368 a(n) = numerator of (n + 3)(n + 4)/((n + 1)(n + 2)).

A027626 Denominator of n(n+5)/((n+2)(n+3)).