A033579 -id:A033579 - cp's OEIS frontend

A201279 a(n) = 6n^2 + 10n + 5.

5, 21, 49, 89, 141, 205, 281, 369, 469, 581, 705, 841, 989, 1149, 1321, 1505, 1701, 1909, 2129, 2361, 2605, 2861, 3129, 3409, 3701, 4005, 4321, 4649, 4989, 5341, 5705, 6081, 6469, 6869, 7281, 7705, 8141, 8589, 9049, 9521, 10005, 10501, 11009, 11529, 12061

Offset: 0

Eleonora Echeverri-Toro, Nov 29 2011

Numbers n where 6n-5 is a square of a number type 6n-1.
Also sequence found by reading the line from 5, in the direction 5, 21,..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Jul 18 2012
The spiral mentioned above naturally appears on a "graphene" like lattice (planar net 6^3). The opposite diagonal is A080859. - Yuriy Sibirmovsky, Oct 04 2016
First differences of A048395. - Leo Tavares, Nov 24 2021 [Corrected by Omar E. Pol, Dec 26 2021]

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Yuriy Sibirmovsky, Diagonals of a 'graphene' number spiral.
Leo Tavares, Illustration: Diamond Frame Stars
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A136392, A080859.

Cf. A003154, A022144, A016754, A046092, A048395.

[6*n^2 + 10*n + 5: n in [0..60]]; // Vincenzo Librandi, Dec 01 2011

LinearRecurrence[{3,-3,1},{5,21,49},50] (* Vincenzo Librandi, Dec 01 2011 *)
Table[6 n^2 + 10 n + 5, {n, 0, 44}] (* or *)
CoefficientList[Series[(1 + x) (5 + x)/(1 - x)^3, {x, 0, 44}], x] (* Michael De Vlieger, Oct 04 2016 *)

a(n)=6*n^2+10*n+5 \\ Charles R Greathouse IV, Nov 29 2011

G.f.: (1+x)*(5+x)/(1-x)^3. - Colin Barker, Jan 09 2012
a(n) = 1 + A033579(n+1). - Omar E. Pol, Jul 18 2012
a(n) = (n+1)*A001844(n+1)-n*A001844(n). [Bruno Berselli, Jan 15 2013]
From Leo Tavares, Nov 24 2021: (Start)
a(n) = A003154(n+2) - A022144(n+1). See Diamond Frame Stars illustration.
a(n) = A016754(n) + A046092(n+1). (End)

A202804 a(n) = n(6n+4).

Original entry on oeis.org

0, 10, 32, 66, 112, 170, 240, 322, 416, 522, 640, 770, 912, 1066, 1232, 1410, 1600, 1802, 2016, 2242, 2480, 2730, 2992, 3266, 3552, 3850, 4160, 4482, 4816, 5162, 5520, 5890, 6272, 6666, 7072, 7490, 7920, 8362, 8816, 9282, 9760, 10250, 10752, 11266, 11792, 12330

Offset: 0

Jeremy Gardiner, Dec 24 2011

Sequence found by reading the line from 0, in the direction 0, 10, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. Opposite numbers to the members of A033579 in the same spiral. - Omar E. Pol, Jul 17 2012

Partial sums give A163815. - Leo Tavares, Feb 25 2022

Jeremy Gardiner, Table of n, a(n) for n = 0..3000
Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Leo Tavares, Illustration: Star Halves.
Pavlos Vavolas, Cellular automaton model of cardiac arrhythmias, University of Sheffield Department of Computer Science (2005), (see page 43). [broken link, abstract]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A003154, A005408, A033580, A033581, A049453, A163815, A195319.

Cf. A001318, A033579, A045944, A080859.

A202804:=n->n*(6*n+4): seq(A202804(n), n=0..100); # Wesley Ivan Hurt, Apr 09 2017

Table[n(6n+4),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,10,32},50] (* Harvey P. Dale, Dec 28 2015 *)

x='x + O('x^50); concat([0], Vec(-2*x*(5 + x)/(x - 1)^3)) \\ Indranil Ghosh, Apr 10 2017

a(n) = 2*n(3*n+2) = 6*n^2 + 4*n = 2*A045944(n).
a(n) = A080859(n) - 1. - Omar E. Pol, Jul 18 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Dec 28 2015
G.f.: 2*x*(5 + x)/(1 - x)^3. - Indranil Ghosh, Apr 10 2017
a(n) = A003154(n+1) - A005408(n). - Leo Tavares, Feb 25 2022
From Amiram Eldar, Mar 01 2022: (Start)
Sum_{n>=1} 1/a(n) = (Pi/sqrt(3) - 3*log(3) + 3)/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(4*sqrt(3)) - 3/8. (End)
E.g.f.: 2*exp(x)*x*(5 + 3*x). - Elmo R. Oliveira, Dec 12 2024

A087348 a(n) = 10n^2 - 6n + 1.

Original entry on oeis.org

5, 29, 73, 137, 221, 325, 449, 593, 757, 941, 1145, 1369, 1613, 1877, 2161, 2465, 2789, 3133, 3497, 3881, 4285, 4709, 5153, 5617, 6101, 6605, 7129, 7673, 8237, 8821, 9425, 10049, 10693, 11357, 12041, 12745, 13469, 14213, 14977, 15761, 16565, 17389, 18233, 19097

Offset: 1

Charlie Marion, Oct 20 2003

Sequence found by reading the line from 5, in the direction 5, 29, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 18 2012

			a(3)=73 since 73^2 = 48^2 + 55^2 = (4*12)^2 + (48 + 7)^2. See 1st formula.

Shawn A. Broyles, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000326, A033567, A033579, A056220, A085787, A153784.

Table[10*n^2 - 6*n + 1, {n, 50}] (* Paolo Xausa, Jul 18 2024 *)

a(n)=10*n^2-6*n+1 \\ Charles R Greathouse IV, Jun 17 2017

a(n)^2 = A033579(n)^2 + A033567(n)^2 = (4*A000326(n))^2 + (A033579(n) + A056220(n-1))^2.
From Colin Barker, Jun 30 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(5 + 14*x + x^2)/(1-x)^3. (End)
a(n) = 1 + A153784(n). - Omar E. Pol, Jul 18 2012
E.g.f.: exp(x)*(10*x^2 + 4*x + 1) - 1. - Elmo R. Oliveira, Oct 31 2024

More terms from Ray Chandler, Oct 22 2003

A153792 12 times pentagonal numbers: a(n) = 6n(3*n-1).

Original entry on oeis.org

0, 12, 60, 144, 264, 420, 612, 840, 1104, 1404, 1740, 2112, 2520, 2964, 3444, 3960, 4512, 5100, 5724, 6384, 7080, 7812, 8580, 9384, 10224, 11100, 12012, 12960, 13944, 14964, 16020, 17112, 18240, 19404, 20604, 21840, 23112, 24420

Offset: 0

Omar E. Pol, Jan 01 2009

For n>=1, a(n) is the first Zagreb index of the triangular grid graph T[n] (see the West reference, p. 390). The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph. - Emeric Deutsch, Nov 10 2016
The M-polynomial of the triangular grid graph T[n] is M(T[n], x, y) = 6*x^2*y^4 + 3*(n-1)*x^4*y^4 +6*(n-2)*x^4*y^6+3*(n-2)*(n-3)*x^6*y^6/2. - Emeric Deutsch, May 09 2018
This is the number of overlapping six sphinx tiled shapes in the sphinx tessellated hexagon described in A291582. - Craig Knecht, Sep 13 2017
a(n) is the number of words of length 3n over the alphabet {a,b,c}, where the number of b's plus the number of c's is 2. - Juan Camacho, Mar 03 2021
Sequence found by reading the line from 0, in the direction 0, 12, ..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - Omar E. Pol, Mar 12 2021

D. B. West, Introduction to Graph Theory, 2nd edition, Prentice-Hall, 2001.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Emeric Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Craig Knecht, Example of 12 overlapping shapes in the order 1 hexagon.
Eric Weisstein's World of Mathematics, Triangular Grid Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A000326, A049450, A062741, A033579, A152743, A153449, A153793.

Cf. A008588, A195160, A195321.

List([0..50],n->6*n*(3*n-1)); # Muniru A Asiru, May 10 2018

seq(6*n*(3*n-1),n=0..50); # Robert Israel, Nov 10 2016

Table[6n(3n-1),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,12,60},40] (* Harvey P. Dale, Mar 11 2012 *)

a(n)=6*n*(3*n-1) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 18*n^2 - 6*n = 12*A000326(n) = 6*A049450(n) = 4*A062741(n) = 3*A033579(n) = 2*A152743(n).
a(n) = 36*n + a(n-1) - 24 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
G.f.: 12*x*(1 + 2*x)/(1-x)^3. - Colin Barker, Feb 14 2012
a(0)=0, a(1)=12, a(2)=60; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 11 2012
E.g.f.: 6*x*(2 + 3*x)*exp(x). - G. C. Greubel, Aug 29 2016
a(n) = A291582(n) - A195321(n) for n > 0. - Craig Knecht, Sep 13 2017
a(n) = A195321(n) - A008588(n). - Omar E. Pol, Mar 12 2021
From Amiram Eldar, May 05 2025: (Start)
Sum_{n>=1} 1/a(n) = log(3)/4 - Pi/(12*sqrt(3)).
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)) - log(2)/3. (End)

A330707 a(n) = ( 3*n^2 + n - 1 + (-1)^floor(n/2) )/4.

Original entry on oeis.org

0, 1, 3, 7, 13, 20, 28, 38, 50, 63, 77, 93, 111, 130, 150, 172, 196, 221, 247, 275, 305, 336, 368, 402, 438, 475, 513, 553, 595, 638, 682, 728, 776, 825, 875, 927, 981, 1036, 1092, 1150, 1210, 1271, 1333, 1397, 1463

Offset: 0

Paul Curtz, Dec 27 2019

Essentially four odds followed by four evens.
Last digit is neither 4 nor 9.
Essentially twice or twin sequences in the hexagonal spiral from A002265.
                  21  21  21  22  22  22  22
                21  14  14  14  14  15  15  23
              20  13   8   8   8   9   9  15  23
            20  13   8   4   4   4   4   9  15  23
          20  13   7   3   1   1   1   5   9  16  23
        20  13   7   3   1   0   0   2   5  10  16  24
          19  12   7   3   0   0   2   5  10  16  24
            19  12   7   3   2   2   5  10  16  24
              19  12   6   6   6   6  10  17  24
                19  12  11  11  11  11  17  25
                  18  18  18  18  17  17  25
.
There are 12 twin sequences. 6 of them (A001859, A006578, A077043, A231559, A024219, A281026) are in the OEIS. a(n) is the seventh.
  0, 1, 3, 7, 13, 20, 28, 38, 50, ...
  1, 2, 4, 6,  7,  8, 10, 12, 13, ...
  1, 2, 2, 1,  1,  2,  2,  1,  1, ... period 4. See A014695.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Cf. A001859, A002265, A006578, A014695, A016921, A024219, A033579, A077043, A231559, A281026.

[(3*n^2+n-1+ (-1)^Floor(n/2))/4: n in [0..60]]; // G. C. Greubel, Dec 30 2019

seq((3*n^2+n-1+sqrt(2)*sin((2*n+1)*Pi/4))/4, n = 0..60); # G. C. Greubel, Dec 30 2019

LinearRecurrence[{3,-4,4,-3,1}, {0,1,3,7,13}, 60] (* Amiram Eldar, Dec 27 2019 *)

concat(0, Vec(x*(1 + 2*x^2) / ((1 - x)^3*(1 + x^2)) + O(x^60))) \\ Colin Barker, Dec 27 2019

[(3*n^2+n-1+(-1)^floor(n/2))/4 for n in (0..60)] # G. C. Greubel, Dec 30 2019

a(n) = A231559(-n).
a(1+2*n) + a(2+2*n) = A033579(n+1).
a(40+n) - a(n) = 1210, 1270, 1330, 1390, 1450, ... . See 10*A016921(n).
From Colin Barker, Dec 27 2019: (Start)
G.f.: x*(1 + 2*x^2) / ((1 - x)^3*(1 + x^2)).
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>4.
(End)
E.g.f.: (cos(x) + sin(x) + (-1 + 4*x + 3*x^2)*exp(x))/4. - Stefano Spezia, Dec 27 2019
a(n) = ( 3*n^2 + n - 1 + sqrt(2)*sin((2*n+1)*Pi/4) )/4 = ( 3*n^2 + n - 1 + (-1)^floor(n/2) )/4. - G. C. Greubel, Dec 30 2019

A174371 a(n) = (6*n-1)^2.

Original entry on oeis.org

1, 25, 121, 289, 529, 841, 1225, 1681, 2209, 2809, 3481, 4225, 5041, 5929, 6889, 7921, 9025, 10201, 11449, 12769, 14161, 15625, 17161, 18769, 20449, 22201, 24025, 25921, 27889, 29929, 32041, 34225, 36481, 38809, 41209, 43681, 46225, 48841, 51529

Offset: 0

Juri-Stepan Gerasimov, Mar 17 2010

Unit together with numbers of form (6*n+5)^2.

Sequence may be obtained by starting with the segment (1, 25) followed by the line from 25 in the direction 25, 121,... in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 29 2016

			a(0)=1 because (6*0-1)^2=1, a(1)=25 because (6*1-1)^2=25.

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

Cf. A016970, A033579.

[(6*n-1)^2: n in [0..50]]; // Vincenzo Librandi, May 07 2011

CoefficientList[Series[(49*x^2 + 22*x + 1)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 27 2013 *)

a(n)=(6*n-1)^2 \\ Charles R Greathouse IV, Jul 28 2016

a(n) = A016970(n-1), n >= 1.
G.f.: (49*x^2 + 22*x + 1)/(1 - x)^3. - Vincenzo Librandi, Jan 27 2013
a(n) = 6*A033579(n) + 1. - Miquel Cerda, Jul 28 2016
a(n) = 36n^2 - 12n + 1. - Omar E. Pol, Jul 28 2016
E.g.f.: exp(x)*(1 + 24*x + 36*x^2). - Stefano Spezia, Aug 19 2023

Offset and formula corrected by R. J. Mathar, Apr 16 2010

A221912 Partial sums of floor(n/12).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 125, 130, 135, 140, 145, 150, 155

Offset: 0

Philippe Deléham, Mar 27 2013

Apart from the initial zeros, the same as A008730.

			..0....0....0....0....0....0....0....0....0....0....0....0
..1....2....3....4....5....6....7....8....9...10...11...12
.14...16...18...20...22...24...26...28...30...32...34...36
.39...42...45...48...51...54...57...60...63...66...69...72
.76...80...84...88...92...96..100..104..108..112..116..120
125..130..135..140..145..150..155..160..165..170..175..180
186..192..198..204..210..216..222..228..234..240..246..252
259..266..273..280..287..294..301..308..315..322..329..336
344..352..360..368..376..384..392..400..408..416..424..432
441..450..459..468..477..486..495..504..513..522..531..540
...

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).

Cf. A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470, A131242, A218530.

Accumulate[Floor[Range[0,70]/12]] (* or *) LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,1,-2,1},{0,0,0,0,0,0,0,0,0,0,0,0,1,2},70] (* Harvey P. Dale, Mar 23 2015 *)

a(12n) = A051866(n).
a(12n+1) = A139267(n).
a(12n+2) = A094159(n).
a(12n+3) = A033579(n).
a(12n+4) = A049452(n).
a(12n+5) = A033581(n).
a(12n+6) = A049453(n).
a(12n+7) = A033580(n).
a(12n+8) = A195319(n).
a(12n+9) = A202804(n).
a(12n+10) = A211014(n).
a(12n+11) = A049598(n).
G.f.: x^12/((1-x)^2*(1-x^12)).
a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=0, a(11)=0, a(12)=1, a(13)=2, a(n)=2*a(n-1)- a(n-2)+ a(n-12)- 2*a(n-13)+ a(n-14). - Harvey P. Dale, Mar 23 2015

A259160 Positive squares (A000290) that are octagonal numbers (A000567) divided by 2.

Original entry on oeis.org

4, 39204, 376437604, 3614553835204, 34706945549192004, 333256087548787788004, 3199924917936514791223204, 30725678728770327476537417604, 295027963953727766493197492611204, 2832858479158015285097354847515364004, 27201106821847298813777034752645032556004

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000290 and A033579 (even octagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			4 is in the sequence because 4 is the 2nd square, and 2*4 is the 2nd octagonal number.

Colin Barker, Table of n, a(n) for n = 1..251
Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

Cf. A000290, A000567, A033579, A259156-A259159, A259161-A259167.

LinearRecurrence[{9603, -9603, 1}, {4, 39204, 376437604}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-4*x*(x^2+198*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))

G.f.: -4*x*(x^2+198*x+1) / ((x-1)*(x^2-9602*x+1)).

A008730 Molien series 1/((1-x)^2(1-x^12)) for 3-dimensional group [2,n] = 22n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 186, 192, 198, 204

Offset: 0

N. J. A. Sloane

			..1....2....3....4....5....6....7....8....9...10...11...12
.14...16...18...20...22...24...26...28...30...32...34...36
.39...42...45...48...51...54...57...60...63...66...69...72
.76...80...84...88...92...96..100..104..108..112..116..120
125..130..135..140..145..150..155..160..165..170..175..180
186..192..198..204..210..216..222..228..234..240..246..252
259..266..273..280..287..294..301..308..315..322..329..336
344..352..360..368..376..384..392..400..408..416..424..432
441..450..459..468..477..486..495..504..513..522..531..540
550..560..570..580..590..600..610..620..630..640..650..660
...
The columns are: A051866, A139267, A094159, A033579, A049452, A033581, A049453, A033580, A195319, A202804, A211014, A049598
- _Philippe Deléham_, Apr 03 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 195
Index entries for Molien series
Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

Cf. A001840, A001972, A008724, A008725, A008726, A008727, A008728, A008729, A008732. - Vladimir Joseph Stephan Orlovsky, Mar 14 2010

Cf. A221912

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^12)) )); // G. C. Greubel, Jul 30 2019

seq(coeff(series(1/(1-x)^2/(1-x^12), x, n+1), x, n), n=0..80);

CoefficientList[Series[1/((1-x)^2*(1-x^12)), {x,0,70}], x] (* Vincenzo Librandi, Jun 11 2013 *)
LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,1,-2,1},{1,2,3,4,5,6,7,8,9,10,11,12,14,16},70] (* Harvey P. Dale, Jan 01 2024 *)

my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^12))) \\ G. C. Greubel, Jul 30 2019

(1/((1-x)^2*(1-x^12))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

G.f. 1/( (1-x)^3 * (1+x) *(1+x+x^2) *(1-x+x^2) * (1+x^2) *(1-x^2+x^4)). - R. J. Mathar, Aug 11 2021
From Mitch Harris, Sep 08 2008: (Start)
a(n) = Sum_{j=0..n+12} floor(j/12).
a(n-12) = (1/2)*floor(n/12)*(2*n - 10 - 12*floor(n/12)). (End)
a(n) = A221912(n+12). - Philippe Deléham, Apr 03 2013

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

A259079 Octagonal numbers (A000567) that are other octagonal numbers divided by 2.

Original entry on oeis.org

280, 373212840, 497012764340408, 661878856450449219400, 881433339438556519000044120, 1173817118196415977287174306335208, 1563188689740940473437573487667885475320, 2081720262768492984525248323578863263574296200

Offset: 1

Colin Barker, Jun 18 2015

Intersection of A000567 and A033579 (even octagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			280 is in the sequence because 280 is the 10th octagonal number, and 2*280 is the 14th octagonal number.

Colin Barker, Table of n, a(n) for n = 1..163
Index entries for linear recurrences with constant coefficients, signature (1331715,-1331715,1).

Cf. A000567, A075528, A107736, A259078.

LinearRecurrence[{1331715,-1331715,1},{280,373212840,497012764340408},20] (* Harvey P. Dale, Dec 04 2015 *)

Vec(-8*x*(x^2+41580*x+35)/((x-1)*(x^2-1331714*x+1)) + O(x^20))

G.f.: -8*x*(x^2+41580*x+35) / ((x-1)*(x^2-1331714*x+1)).

cp's OEIS Frontend

A201279 a(n) = 6n^2 + 10n + 5.

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A202804 a(n) = n*(6*n+4).

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Maple

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A087348 a(n) = 10*n^2 - 6*n + 1.

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A153792 12 times pentagonal numbers: a(n) = 6*n*(3*n-1).

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A330707 a(n) = ( 3*n^2 + n - 1 + (-1)^floor(n/2) )/4.

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A174371 a(n) = (6*n-1)^2.

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Magma

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A202804 a(n) = n(6n+4).

A087348 a(n) = 10n^2 - 6n + 1.

A153792 12 times pentagonal numbers: a(n) = 6n(3*n-1).

A008730 Molien series 1/((1-x)^2(1-x^12)) for 3-dimensional group [2,n] = 22n.