A139580 -id:A139580 - cp's OEIS frontend

A139579 a(n) = 2n^2 + 15n.

0, 17, 38, 63, 92, 125, 162, 203, 248, 297, 350, 407, 468, 533, 602, 675, 752, 833, 918, 1007, 1100, 1197, 1298, 1403, 1512, 1625, 1742, 1863, 1988, 2117, 2250, 2387, 2528, 2673, 2822, 2975, 3132, 3293, 3458, 3627, 3800, 3977, 4158, 4343, 4532, 4725, 4922, 5123, 5328, 5537

Offset: 0

Omar E. Pol, May 19 2008

Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139580, A139581.

LinearRecurrence[{3,-3,1},{0,17,38},50] (* Stefano Spezia, Oct 21 2023 *)

a(n)=2*n^2+15*n \\ Charles R Greathouse IV, Jun 17 2017

a(n) = a(n-1) + 4*n + 13; a(0) = 0. - Vincenzo Librandi, Nov 24 2010
From Stefano Spezia, Oct 21 2023: (Start)
O.g.f.: x*(17 - 13*x)/(1 - x)^3.
E.g.f.: exp(x)*x*(17 + 2*x). (End)
From Amiram Eldar, Nov 10 2023: (Start)
Sum_{n>=1} 1/a(n) = 182144/675675 - 2*log(2)/15.
Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/15 - Pi/30 + 67952/675675. (End)

A139576 a(n) = n(2n + 9).

Original entry on oeis.org

0, 11, 26, 45, 68, 95, 126, 161, 200, 243, 290, 341, 396, 455, 518, 585, 656, 731, 810, 893, 980, 1071, 1166, 1265, 1368, 1475, 1586, 1701, 1820, 1943, 2070, 2201, 2336, 2475, 2618, 2765, 2916, 3071, 3230, 3393, 3560, 3731, 3906

Offset: 0

Omar E. Pol, May 19 2008

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

Cf. A014105, A014106, A033537, A130861, A139577, A139578, A139579, A139580, A139581.

Cf. A277979.

s=0;lst={s};Do[s+=n++ +11;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[Sum[(2*i + n - 1), {i, 4, n}], {n, 3, 45}] (* Zerinvary Lajos, Jul 11 2009 *)
Table[n(2n+9),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,11,26},50] (* Harvey P. Dale, Dec 18 2018 *)

a(n)=n*(2*n+9) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 9*n.
a(n) = a(n-1) + 4*n + 7 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(11 - 7*x)/(1-x)^3.
E.g.f.: exp(x)*x*(11 + 2*x).
a(n) = A277979(n)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139577 a(n) = n(2n + 11).

Original entry on oeis.org

0, 13, 30, 51, 76, 105, 138, 175, 216, 261, 310, 363, 420, 481, 546, 615, 688, 765, 846, 931, 1020, 1113, 1210, 1311, 1416, 1525, 1638, 1755, 1876, 2001, 2130, 2263, 2400, 2541, 2686, 2835, 2988, 3145, 3306, 3471, 3640, 3813, 3990

Offset: 0

Omar E. Pol, May 19 2008

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

Cf. A014105, A014106, A033537, A130861, A139576, A139578, A139579, A139580, A139581.

s=0;lst={s};Do[s+=n++ +13;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(2n+11),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,30},50] (* Harvey P. Dale, Mar 17 2019 *)

a(n)=n*(2*n+11) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 11*n.
a(n) = a(n-1) + 4*n + 9 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(13 - 9*x)/(1-x)^3.
E.g.f.: exp(x)*x*(13 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139578 a(n) = n(2n + 13).

Original entry on oeis.org

0, 15, 34, 57, 84, 115, 150, 189, 232, 279, 330, 385, 444, 507, 574, 645, 720, 799, 882, 969, 1060, 1155, 1254, 1357, 1464, 1575, 1690, 1809, 1932, 2059, 2190, 2325, 2464, 2607, 2754, 2905, 3060, 3219, 3382, 3549, 3720, 3895, 4074, 4257, 4444, 4635, 4830, 5029

Offset: 0

Omar E. Pol, May 19 2008

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

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139579, A139580, A139581.

s=0;lst={s};Do[s+=n++ +15;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(2n+13),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,15,34},50] (* Harvey P. Dale, Nov 22 2014 *)

a(n)=n*(2*n+13) \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 2*n^2 + 13*n.
a(n) = a(n-1) + 4*n + 11 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(15 - 11*x)/(1 - x)^3.
E.g.f.: exp(x)*x*(15 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A139581 a(n) = n(2n + 19).

Original entry on oeis.org

0, 21, 46, 75, 108, 145, 186, 231, 280, 333, 390, 451, 516, 585, 658, 735, 816, 901, 990, 1083, 1180, 1281, 1386, 1495, 1608, 1725, 1846, 1971, 2100, 2233, 2370, 2511, 2656, 2805, 2958, 3115, 3276, 3441, 3610, 3783, 3960, 4141

Offset: 0

Omar E. Pol, May 19 2008

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

Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139580.

Table[n(2n+19),{n,0,50}]  (* Harvey P. Dale, Jan 26 2011 *)

a(n)=n*(2*n+19) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 2*n^2 + 19*n.
a(n) = a(n-1) + 4*n + 17 (with a(0)=0). - Vincenzo Librandi, Nov 24 2010
From Elmo R. Oliveira, Nov 29 2024: (Start)
G.f.: x*(21 - 17*x)/(1-x)^3.
E.g.f.: exp(x)*x*(21 + 2*x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

cp's OEIS Frontend

A139579 a(n) = 2*n^2 + 15*n.

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A139576 a(n) = n*(2*n + 9).

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A139577 a(n) = n*(2*n + 11).

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A139578 a(n) = n*(2*n + 13).

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A139581 a(n) = n*(2*n + 19).

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Formula

A139579 a(n) = 2n^2 + 15n.

A139576 a(n) = n(2n + 9).

A139577 a(n) = n(2n + 11).

A139578 a(n) = n(2n + 13).

A139581 a(n) = n(2n + 19).