A022289 -id:A022289 - cp's OEIS frontend

A022275 a(n) = n(17n + 1)/2.

0, 9, 35, 78, 138, 215, 309, 420, 548, 693, 855, 1034, 1230, 1443, 1673, 1920, 2184, 2465, 2763, 3078, 3410, 3759, 4125, 4508, 4908, 5325, 5759, 6210, 6678, 7163, 7665, 8184, 8720, 9273, 9843, 10430, 11034, 11655, 12293, 12948, 13620, 14309, 15015

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A022274.

Cf. similar sequences listed in A022289.

[n*(17*n + 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Table[n (17 n + 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 9, 35}, 40] (* Harvey P. Dale, May 06 2013 *)
CoefficientList[Series[x (9 + 8 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)

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

a(n) = 17*n + a(n-1) - 8 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
a(0)=0, a(1)=9, a(2)=35; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 06 2013
G.f.: x*(9+8*x)/(1-x)^3. - Vincenzo Librandi, Mar 31 2015
a(n) = A022274(-n). - Bruno Berselli, Mar 31 2015
a(n) = A000217(9*n) - A000217(8*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(17*x + 18)*exp(x). - G. C. Greubel, Aug 23 2017

More terms from Vincenzo Librandi, Mar 31 2015

A022277 a(n) = n(19n + 1)/2.

Original entry on oeis.org

0, 10, 39, 87, 154, 240, 345, 469, 612, 774, 955, 1155, 1374, 1612, 1869, 2145, 2440, 2754, 3087, 3439, 3810, 4200, 4609, 5037, 5484, 5950, 6435, 6939, 7462, 8004, 8565, 9145, 9744, 10362, 10999, 11655, 12330, 13024, 13737, 14469, 15220, 15990, 16779, 17587, 18414

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A022276.

Cf. similar sequences listed in A022289.

[n*(19*n + 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015

Table[n (19 n + 1)/2, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
CoefficientList[Series[x (10 + 9 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3,-3,1},{0,10,39},50] (* Harvey P. Dale, May 02 2021 *)

a(n)=n*(19*n+1)/2 \\ Charles R Greathouse IV, Mar 07 2011

a(n) = 19*n + a(n-1) - 9 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
G.f.: x*(10 + 9*x)/(1 - x)^3. - Vincenzo Librandi, Mar 31 2015
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. - Vincenzo Librandi, Mar 31 2015
a(n) = A022276(-n). - Bruno Berselli, Apr 01 2015
a(n) = A000217(10*n) - A000217(9*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(19*x + 20)*exp(x). - G. C. Greubel, Aug 23 2017

More terms from Vincenzo Librandi, Mar 31 2015

A022285 a(n) = n(27n + 1)/2.

Original entry on oeis.org

0, 14, 55, 123, 218, 340, 489, 665, 868, 1098, 1355, 1639, 1950, 2288, 2653, 3045, 3464, 3910, 4383, 4883, 5410, 5964, 6545, 7153, 7788, 8450, 9139, 9855, 10598, 11368, 12165, 12989, 13840, 14718, 15623

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. similar sequences listed in A022289.

A022285:=n->n*(27*n+1)/2; seq(A022285(k), k=0..100); # Wesley Ivan Hurt, Nov 04 2013

Table[n (27 n + 1)/2, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 14, 55}, 40] (* Harvey P. Dale, Sep 20 2011 *)

a(n)=n*(27*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = a(n-1) + 27*n - 13 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
a(0)=0, a(1)=14, a(2)=55; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). -Harvey P. Dale, Sep 20 2011
G.f.: x*(13*x + 14)/(1-x)^3. - Harvey P. Dale, Sep 20 2011
a(n) = 12/(n+2)!*Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(j+n)^(n+2). - Vladimir Kruchinin, Jun 04 2013
a(n) = A000217(14*n) - A000217(13*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(27*x + 28)*exp(x). - G. C. Greubel, Aug 23 2017

A022287 a(n) = n(29n + 1)/2.

Original entry on oeis.org

0, 15, 59, 132, 234, 365, 525, 714, 932, 1179, 1455, 1760, 2094, 2457, 2849, 3270, 3720, 4199, 4707, 5244, 5810, 6405, 7029, 7682, 8364, 9075, 9815, 10584, 11382, 12209, 13065, 13950, 14864, 15807, 16779

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. similar sequences listed in A022289.

Table[n (29 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)

a(n)=n*(29*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 29*n + a(n-1) - 14 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
G.f.: x*(15 + 14*x)/(1 - x)^3 . - R. J. Mathar, Aug 04 2016
a(n) = A000217(15*n) - A000217(14*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(29*x + 30)*exp(x). - G. C. Greubel, Aug 24 2017

A022279 a(n) = n(21n + 1)/2.

Original entry on oeis.org

0, 11, 43, 96, 170, 265, 381, 518, 676, 855, 1055, 1276, 1518, 1781, 2065, 2370, 2696, 3043, 3411, 3800, 4210, 4641, 5093, 5566, 6060, 6575, 7111, 7668, 8246, 8845, 9465, 10106, 10768, 11451, 12155

Offset: 0

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

Cf. similar sequences listed in A022289.

Table[n (21 n + 1)/2, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 11, 43}, 40] (* Harvey P. Dale, May 06 2014 *)

a(n)=n*(21*n+1)/2 \\ Charles R Greathouse IV, Jun 16 2017

a(n) = 21*n + a(n-1) - 10 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
a(0)=0, a(1)=11, a(2)=43; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 06 2014
a(n) = A000217(11*n) - A000217(10*n). - Bruno Berselli, Oct 13 2016
From G. C. Greubel, Aug 23 2017: (Start)
G.f.: x*(10*x + 11)/(1-x)^3.
E.g.f.: (x/2)*(21*x + 22)*exp(x). (End)

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A022275 a(n) = n*(17*n + 1)/2.

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A022277 a(n) = n*(19*n + 1)/2.

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Magma

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A022285 a(n) = n*(27*n + 1)/2.

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A022287 a(n) = n*(29*n + 1)/2.

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A022279 a(n) = n*(21*n + 1)/2.

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A022275 a(n) = n(17n + 1)/2.

A022277 a(n) = n(19n + 1)/2.

A022285 a(n) = n(27n + 1)/2.

A022287 a(n) = n(29n + 1)/2.

A022279 a(n) = n(21n + 1)/2.