A261191 -id:A261191 - cp's OEIS frontend

A282853 36-gonal numbers: a(n) = n(17n-16).

0, 1, 36, 105, 208, 345, 516, 721, 960, 1233, 1540, 1881, 2256, 2665, 3108, 3585, 4096, 4641, 5220, 5833, 6480, 7161, 7876, 8625, 9408, 10225, 11076, 11961, 12880, 13833, 14820, 15841, 16896, 17985, 19108, 20265, 21456, 22681, 23940, 25233

Offset: 0

So Jung Kim, Feb 23 2017

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A254474, A261191, A001107.

Table[n(34n-32)/2, {n,50}]
PolygonalNumber[36,Range[0,50]] (* or *) LinearRecurrence[{3,-3,1},{0,1,36},50] (* Harvey P. Dale, Apr 18 2025 *)

for(n=0,100,print1(n*(17*n-16),", ")) \\ Derek Orr, Feb 27 2017

From Nikolaos Pantelidis, Feb 09 2023 : (Start)
G.f.: x*(1 + 33*x)/(1 - x)^3.
E.g.f.: exp(x)*(x + 17*x^2). (End)

A282850 38-gonal numbers: a(n) = n(18n-17).

Original entry on oeis.org

0, 1, 38, 111, 220, 365, 546, 763, 1016, 1305, 1630, 1991, 2388, 2821, 3290, 3795, 4336, 4913, 5526, 6175, 6860, 7581, 8338, 9131, 9960, 10825, 11726, 12663, 13636, 14645, 15690, 16771, 17888, 19041, 20230, 21455, 22716, 24013, 25346, 26715, 28120, 29561

Offset: 0

Haney Moon, Feb 23 2017

Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A255187, A254474, A261191.

Table[n(36n-34)/2, {n,50}]
LinearRecurrence[{3, -3, 1}, {0, 1, 38}, 42] (* or *) CoefficientList[Series[-x * (35 * x + 1) / (x - 1) ^ 3, {x, 0, 41}], x] (* Indranil Ghosh, Feb 27 2017 *)

for(n=0,20,print1(n*(18*n-17),", ")) \\ Derek Orr, Feb 26 2017

a(n)=n*(18*n-17) \\ Charles R Greathouse IV, Feb 26 2017

G.f.: -x*(35*x+1)/(x-1)^3.

E.g.f.: exp(x)*(x + 18*x^2). - Nikolaos Pantelidis, Feb 10 2023

A282851 35-gonal numbers: a(n) = n(33n-31)/2.

Original entry on oeis.org

0, 1, 35, 102, 202, 335, 501, 700, 932, 1197, 1495, 1826, 2190, 2587, 3017, 3480, 3976, 4505, 5067, 5662, 6290, 6951, 7645, 8372, 9132, 9925, 10751, 11610, 12502, 13427, 14385, 15376, 16400, 17457, 18547, 19670, 20826, 22015, 23237, 24492

Offset: 0

Kyu Bin Choi, Feb 23 2017

Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A255187, A254474, A261191.

Table[n(33n-31)/2, {n, 50}]
PolygonalNumber[35,Range[0,40]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 12 2017 *)

for(n=0,100,print1(n*(33*n-31)/2,", ")) \\ Derek Orr, Feb 27 2017

From Nikolaos Pantelidis, Feb 10 2023: (Start)
G.f.: x*(1 + 32*x)/(1 - x)^3.
E.g.f.: exp(x)*(x + 33*x^2/2). (End)

A282854 34-gonal numbers: a(n) = n(32n-30)/2.

Original entry on oeis.org

0, 1, 34, 99, 196, 325, 486, 679, 904, 1161, 1450, 1771, 2124, 2509, 2926, 3375, 3856, 4369, 4914, 5491, 6100, 6741, 7414, 8119, 8856, 9625, 10426, 11259, 12124, 13021, 13950, 14911, 15904, 16929, 17986, 19075, 20196, 21349, 22534, 23751

Offset: 0

Daniel Mohebiravesh, Feb 23 2017

Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A246645, A254474, A261191.

Table[n(32n-30)/2, {n,50}]
PolygonalNumber[34,Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,1,34},40] (* The first program requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 26 2018 *)

a(n)=n*(16*n-15) \\ Charles R Greathouse IV, Feb 27 2017

From Nikolaos Pantelidis, Feb 09 2023 : (Start)
G.f.: x*(1 + 31*x)/(1 - x)^3.
E.g.f.: exp(x)*(x + 16*x^2). (End)

cp's OEIS Frontend

A282853 36-gonal numbers: a(n) = n*(17*n-16).

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A282850 38-gonal numbers: a(n) = n*(18*n-17).

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A282851 35-gonal numbers: a(n) = n*(33*n-31)/2.

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A282854 34-gonal numbers: a(n) = n*(32*n-30)/2.

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A282853 36-gonal numbers: a(n) = n(17n-16).

A282850 38-gonal numbers: a(n) = n(18n-17).

A282851 35-gonal numbers: a(n) = n(33n-31)/2.

A282854 34-gonal numbers: a(n) = n(32n-30)/2.