A162499 -id:A162499 - cp's OEIS frontend

A162736 G.f. is the polynomial (Product_{k=1..30} (1 - x^(3*k)))/(1-x)^30.

1, 30, 465, 4959, 40890, 277791, 1618199, 8306730, 38329299, 161383520, 627356796, 2272915164, 7734020120, 24874638204, 76028550900, 221849950497, 620471946324, 1669004265525, 4330837858674, 10869702783150, 26449453637412

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..1365 (terms 0..1000 from Harvey P. Dale)

m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..30]])/(1-x)^30; Coefficients(R!(F)); // G. C. Greubel, Jul 07 2018

CoefficientList[Series[Times@@(1-x^Range[3,90,3])/(1-x)^30,{x,0,20}],x] (* Harvey P. Dale, Oct 04 2011 *)

x='x+O('x^50); A = prod(k=1, 30, (1-x^(3*k)))/(1-x)^30; Vec(A) \\ G. C. Greubel, Jul 07 2018

A162500 Expansion of the polynomial (1-x^3) * (1-x^6) * (1-x^9) / (1-x)^3.

Original entry on oeis.org

1, 3, 6, 9, 12, 15, 17, 18, 18, 17, 15, 12, 9, 6, 3, 1

Offset: 0

N. J. A. Sloane, Dec 02 2009

This is a row of the triangle A162499.

Only finitely many terms are nonzero.

Cf. A162499.

m:=16; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)/(1-x)^3)); /* complete row without zeros */ // G. C. Greubel, Jul 06 2018

m:=3: seq(coeff(series(mul((1-x^(3*i)),i=1..m)/(1-x)^m, x,n+1),x,n),n=0..16); # Muniru A Asiru, Jul 07 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@3))/(1 - x)^3, {x, 0, 40}], x] (* Wesley Ivan Hurt, Sep 13 2014 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^16); Vec((1-x^3)*(1-x^6)*(1-x^9)/(1-x)^3) \\ G. C. Greubel, Jul 06 2018

A162539 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) / (1-x)^6.

Original entry on oeis.org

1, 6, 21, 55, 120, 231, 405, 660, 1014, 1484, 2085, 2829, 3724, 4773, 5973, 7315, 8784, 10359, 12013, 13713, 15420, 17091, 18681, 20145, 21440, 22527, 23373, 23952, 24246, 24246, 23952, 23373, 22527, 21440, 20145, 18681, 17091, 15420, 13713

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..57

m:=58; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)/(1-x)^6)); /* complete row */ // G. C. Greubel, Jul 06 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@6))/(1 - x)^6, {x, 0, 70}], x] (* G. C. Greubel, Jul 06 2018 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^58); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)/(1-x)^6) /* complete row */ \\ G. C. Greubel, Jul 06 2018

A162595 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) / (1-x)^7.

Original entry on oeis.org

1, 7, 28, 83, 203, 434, 839, 1499, 2513, 3997, 6082, 8911, 12635, 17408, 23381, 30696, 39480, 49839, 61852, 75565, 90985, 108075, 126750, 146874, 168259, 190666, 213808, 237355, 260941, 284173, 306641, 327929, 347627, 365343, 380715, 393423

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..77 (complete row)

Cf. A162499.

m:=50; R:=PowerSeriesRing(Integers(), m); F:=(&*[(1-x^(3*k)): k in [1..7]])/(1-x)^7; Coefficients(R!(F)); // G. C. Greubel, Jul 07 2018

CoefficientList[Series[Times@@(1-x^(3*Range[7]))/(1-x)^7,{x,0,40}],x] (* Harvey P. Dale, Oct 08 2015 *)

x='x+O('x^50); A = prod(k=1, 7, (1-x^(3*k)))/(1-x)^7; Vec(A) \\ G. C. Greubel, Jul 07 2018

A162596 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) / (1-x)^8.

Original entry on oeis.org

1, 8, 36, 119, 322, 756, 1595, 3094, 5607, 9604, 15686, 24597, 37232, 54640, 78021, 108717, 148197, 198036, 259888, 335453, 426438, 534513, 661263, 808137, 976395, 1167054, 1380834, 1618106, 1878844, 2162583, 2468385, 2794815, 3139929

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..100 (complete row)

m:=100; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1- x^18)*(1-x^21)*(1-x^24)/(1-x)^8)); // G. C. Greubel, Jul 06 2018

CoefficientList[Series[Times@@(1-x^(3*Range[8]))/(1-x)^8,{x,0,40}],x] (* Harvey P. Dale, Jun 03 2012 *)

x='x+O('x^100); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1- x^18)*(1-x^21)*(1-x^24)/(1-x)^8) \\ G. C. Greubel, Jul 06 2018

A162602 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) / (1-x)^9.

Original entry on oeis.org

1, 9, 45, 164, 486, 1242, 2837, 5931, 11538, 21142, 36828, 61425, 98657, 153297, 231318, 340035, 488232, 686268, 946156, 1281609, 1708047, 2242560, 2903823, 3711960, 4688355, 5855409, 7236243, 8854348, 10733184, 12895731, 15363997

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..126

m:=127; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)/(1-x)^9)); // G. C. Greubel, Jul 06 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@9))/(1 - x)^9, {x, 0, 70}], x] (* G. C. Greubel, Jul 06 2018 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^127); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)/(1-x)^9) \\ G. C. Greubel, Jul 06 2018

A162617 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) / (1-x)^10.

Original entry on oeis.org

1, 10, 55, 219, 705, 1947, 4784, 10715, 22253, 43395, 80223, 141648, 240305, 393602, 624920, 964955, 1453187, 2139455, 3085611, 4367220, 6075267, 8317827, 11221650, 14933610, 19621965, 25477374, 32713617, 41567965, 52301149, 65196880

Offset: 0

N. J. A. Sloane, Dec 02 2009

This is a row of the triangle in A162499.

Only finitely many terms are nonzero.

Vincenzo Librandi, Table of n, a(n) for n = 0..155 (complete sequence)

m:=155; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)/(1-x)^10)); /* complete row */ // G. C. Greubel, Jul 06 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@10))/(1 - x)^10, {x, 0, 70}], x] (* Vincenzo Librandi, Mar 14 2013 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^155); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)/(1-x)^10) /* complete row */ \\ G. C. Greubel, Jul 06 2018

A162628 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) / (1-x)^11.

Original entry on oeis.org

1, 11, 66, 285, 990, 2937, 7721, 18436, 40689, 84084, 164307, 305955, 546260, 939862, 1564782, 2529737, 3982924, 6122379, 9207990, 13575210, 19650477, 27968304, 39189954, 54123564, 73745529, 99222903, 131936520, 173504485

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..187

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1- x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)/(1-x)^11)); // G. C. Greubel, Jul 06 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@11))/(1 - x)^11, {x, 0, 70}], x] (* G. C. Greubel, Jul 06 2018 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^50); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1- x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)/(1-x)^11) \\ G. C. Greubel, Jul 06 2018

A162629 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) * (1-x^36) / (1-x)^12.

Original entry on oeis.org

1, 12, 78, 363, 1353, 4290, 12011, 30447, 71136, 155220, 319527, 625482, 1171742, 2111604, 3676386, 6206123, 10189047, 16311426, 25519416, 39094626, 58745103, 86713407, 125903361, 180026925, 253772454, 352995357, 484931877, 658436362

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..222

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)*(1-x^36)/(1-x)^12)); // G. C. Greubel, Jul 06 2018

CoefficientList[ Series[Times @@ (1 - x^(3 Range@12))/(1 - x)^12, {x, 0, 70}], x] (* G. C. Greubel, Jul 06 2018 and slightly modified by Robert G. Wilson v, Jul 23 2018 *)

x='x+O('x^50); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)*(1-x^36)/(1-x)^12) \\ G. C. Greubel, Jul 06 2018

A162631 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) * (1-x^36) * (1-x^39) / (1-x)^13.

Original entry on oeis.org

1, 13, 91, 454, 1807, 6097, 18108, 48555, 119691, 274911, 594438, 1219920, 2391662, 4503266, 8179652, 14385775, 24574822, 40886248, 66405664, 105500290, 164245393, 250958800, 376862161, 556889086, 810661540, 1163656897

Offset: 0

N. J. A. Sloane, Dec 02 2009

nonn

This is a row of the triangle in A162499. Only finitely many terms are nonzero.

G. C. Greubel, Table of n, a(n) for n = 0..260

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)*(1-x^36)*(1-x^39)/(1-x)^13)); // G. C. Greubel, Jul 06 2018

CoefficientList[Series[(Times@@(1-x^(3*Range[13])))/(1-x)^13,{x,0,30}],x] (* Harvey P. Dale, May 09 2016 *)

x='x+O('x^50); Vec((1-x^3)*(1-x^6)*(1-x^9)*(1-x^12)*(1-x^15)*(1-x^18)*(1-x^21)*(1-x^24)*(1-x^27)*(1-x^30)*(1-x^33)*(1-x^36)*(1-x^39)/(1-x)^13) \\ G. C. Greubel, Jul 06 2018

cp's OEIS Frontend

A162736 G.f. is the polynomial (Product_{k=1..30} (1 - x^(3*k)))/(1-x)^30.

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A162500 Expansion of the polynomial (1-x^3) * (1-x^6) * (1-x^9) / (1-x)^3.

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A162539 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) / (1-x)^6.

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A162595 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) / (1-x)^7.

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A162596 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) / (1-x)^8.

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A162602 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) / (1-x)^9.

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A162617 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) / (1-x)^10.

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A162628 G.f. is the polynomial (1-x^3) * (1-x^6) * (1-x^9) * (1-x^12) * (1-x^15) * (1-x^18) * (1-x^21) * (1-x^24) * (1-x^27) * (1-x^30) * (1-x^33) / (1-x)^11.

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