A022269 -id:A022269 - cp's OEIS frontend

A026817 Duplicate of A022269.

6, 23, 51, 90, 140, 201, 273, 356, 450, 555, 671, 798, 936, 1085, 1245, 1416, 1598, 1791, 1995, 2210, 2436, 2673, 2921, 3180, 3450, 3731, 4023, 4326, 4640, 4965, 5301, 5648, 6006, 6375, 6755, 7146, 7548, 7961, 8385, 8820, 9266, 9723, 10191

Offset: 1

dead

A022289 a(n) = n(31n + 1)/2.

Original entry on oeis.org

0, 16, 63, 141, 250, 390, 561, 763, 996, 1260, 1555, 1881, 2238, 2626, 3045, 3495, 3976, 4488, 5031, 5605, 6210, 6846, 7513, 8211, 8940, 9700, 10491, 11313, 12166, 13050, 13965, 14911, 15888, 16896, 17935

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 of the form n*((2*k+1)*n + 1)/2: A000217 (k=0), A005449 (k=1), A005475 (k=2), A022265 (k=3), A022267 (k=4), A022269 (k=5), A022271 (k=6), A022273 (k=7), A022275 (k=8), A022277 (k=9), A022279 (k=10), A022281 (k=11), A022283 (k=12), A022285 (k=13), A022287 (k=14), this sequence (k=15).

Table[n (31 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)
LinearRecurrence[{3,-3,1},{0,16,63},40] (* Harvey P. Dale, Aug 10 2019 *)

a(n)=n*(31*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 31*n + a(n-1) - 15, for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
G.f.: x*(16 + 15*x)/(1 - x)^3 . - R. J. Mathar, Sep 02 2016
a(n) = A000217(16*n) - A000217(15*n). In general, n*((2*k+1)*n + 1)/2 = A000217((k+1)*n) - A000217(k*n). - Bruno Berselli, Oct 13 2016
E.g.f.: (x/2)*(31*x + 32)*exp(x). - G. C. Greubel, Aug 23 2017

A110449 Triangle read by rows: T(n,k) = n((2k+1)*n+1)/2, 0<=k<=n.

Original entry on oeis.org

0, 1, 2, 3, 7, 11, 6, 15, 24, 33, 10, 26, 42, 58, 74, 15, 40, 65, 90, 115, 140, 21, 57, 93, 129, 165, 201, 237, 28, 77, 126, 175, 224, 273, 322, 371, 36, 100, 164, 228, 292, 356, 420, 484, 548, 45, 126, 207, 288, 369, 450, 531, 612, 693, 774, 55, 155, 255, 355, 455, 555, 655, 755, 855, 955, 1055

Offset: 0

Reinhard Zumkeller, Jul 21 2005

Row sums give A110450; central terms give A110451;
T(n,0) = A000217(n);
T(n,1) = A005449(n) for n>0;
T(n,2) = A005475(n) for n>1;
T(n,3) = A022265(n) for n>2;
T(n,4) = A022267(n) for n>3;
T(n,5) = A022269(n) for n>4;
T(n,6) = A022271(n) for n>5;
T(n,7) = A022263(n) for n>6;
T(n+1,n-1) = A059270(n) for n>1;
T(n,n-1) = A081436(n) for n>1;
T(n,n) = A085786(n).

			Triangle starts:
0;
1, 2;
3, 7, 11;
6, 15, 24, 33;
10, 26, 42, 58, 74;
...

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Cf. A126890.

Table[n*((2*k + 1)*n + 1)/2, {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 23 2017 *)

tabl(nn) = {for (n=0, nn, for (k=0, n, print1(n*((2*k+1)*n+1)/2, ", ");); print(););} \\ Michel Marcus, Jun 22 2015

T(n,k) = n*((2*k + 1)*n + 1)/2, 0 <= k <= n.

A254963 a(n) = n(11n + 3)/2.

Original entry on oeis.org

0, 7, 25, 54, 94, 145, 207, 280, 364, 459, 565, 682, 810, 949, 1099, 1260, 1432, 1615, 1809, 2014, 2230, 2457, 2695, 2944, 3204, 3475, 3757, 4050, 4354, 4669, 4995, 5332, 5680, 6039, 6409, 6790, 7182, 7585, 7999, 8424, 8860, 9307, 9765, 10234, 10714, 11205, 11707

Offset: 0

Bruno Berselli, Feb 11 2015

This sequence provides the first differences of A254407 and the partial sums of A017473.
Also:
a(n) - n         = A022269(n);
a(n) + n         = n*(11*n+5)/2: 0, 8, 27, 57, 98, 150, 213, 287, ...;
a(n) - 2*n       = A022268(n);
a(n) + 2*n       = n*(11*n+7)/2: 0, 9, 29, 60, 102, 155, 219, 294, ...;
a(n) - 3*n       = n*(11*n-3)/2: 0, 4, 19, 45, 82, 130, 189, 259, ...;
a(n) + 3*n       = A211013(n);
a(n) - 4*n       = A226492(n);
a(n) + 4*n       = A152740(n);
a(n) - 5*n       = A180223(n);
a(n) + 5*n       = n*(11*n+13)/2: 0, 12, 35, 69, 114, 170, 237, 315, ...;
a(n) - 6*n       = A051865(n);
a(n) + 6*n       = n*(11*n+15)/2: 0, 13, 37, 72, 118, 175, 243, 322, ...;
a(n) - 7*n       = A152740(n-1) with A152740(-1) = 0;
a(n) + 7*n       = n*(11*n+17)/2: 0, 14, 39, 75, 122, 180, 249, 329, ...;
a(n) - n*(n-1)/2 = A168668(n);
a(n) + n*(n-1)/2 = A049453(n);
a(n) - n*(n+1)/2 = A202803(n);
a(n) + n*(n+1)/2 = A033580(n).

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

Cf. A008729 and A218530 (seventh column); A017473, A254407.
Cf. similar sequences of the type 4*n^2 + k*n*(n+1)/2: A055999 (k=-7, n>6), A028552 (k=-6, n>2), A095794 (k=-5, n>1), A046092 (k=-4, n>0), A000566 (k=-3), A049450 (k=-2), A022264 (k=-1), A016742 (k=0), A022267 (k=1), A202803 (k=2), this sequence (k=3), A033580 (k=4).
Cf. A069125: (2*n+1)^2 + 3*n*(n+1)/2; A147875: n^2 + 3*n*(n+1)/2.
Cf. A022268, A022269, A049453, A051865, A152740, A168668, A180223, A211013, A226492.

Magma
```
[n*(11*n+3)/2: n in [0..50]];
```

Table[n (11 n + 3)/2, {n, 0, 50}]
LinearRecurrence[{3,-3,1},{0,7,25},50] (* Harvey P. Dale, Mar 25 2018 *)

Maxima
```
makelist(n*(11*n+3)/2, n, 0, 50);
```
PARI
```
vector(50, n, n--; n*(11*n+3)/2)
```
Sage
```
[n*(11*n+3)/2 for n in (0..50)]
```

G.f.: x*(7 + 4*x)/(1 - x)^3.
From Elmo R. Oliveira, Dec 15 2024: (Start)
E.g.f.: exp(x)*x*(14 + 11*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A226492 a(n) = n(11n-5)/2.

Original entry on oeis.org

0, 3, 17, 42, 78, 125, 183, 252, 332, 423, 525, 638, 762, 897, 1043, 1200, 1368, 1547, 1737, 1938, 2150, 2373, 2607, 2852, 3108, 3375, 3653, 3942, 4242, 4553, 4875, 5208, 5552, 5907, 6273, 6650, 7038, 7437, 7847, 8268, 8700, 9143, 9597, 10062, 10538, 11025, 11523

Offset: 0

Bruno Berselli, Jun 11 2013

Sequences of numbers of the form n*(n*k - k + 6)/2:
. k from 0 to 10, respectively: A008585, A055998, A005563, A045943, A014105, A005475, A033428, A022264, A033991, A062741, A147874;
. k=11: a(n);
. k=12: A094159;
. k=13: 0, 3, 19, 48, 90, 145, 213, 294, 388, 495, 615, 748, 894, ...;
. k=14: 0, 3, 20, 51, 96, 155, 228, 315, 416, 531, 660, 803, 960, ...;
. k=15: A152773;
. k=16: A139272;
. k=17: 0, 3, 23, 60, 114, 185, 273, 378, 500, 639, 795, 968, ...;
. k=18: A152751;
. k=19: 0, 3, 25, 66, 126, 205, 303, 420, 556, 711, 885, 1078, ...;
. k=20: 0, 3, 26, 69, 132, 215, 318, 441, 584, 747, 930, 1133, ...;
. k=21: A152759;
. k=22: 0, 3, 28, 75, 144, 235, 348, 483, 640, 819, 1020, 1243, ...;
. k=23: 0, 3, 29, 78, 150, 245, 363, 504, 668, 855, 1065, 1298, ...;
. k=24: A152767;
. k=25: 0, 3, 31, 84, 162, 265, 393, 546, 724, 927, 1155, 1408, ...;
. k=26: 0, 3, 32, 87, 168, 275, 408, 567, 752, 963, 1200, 1463, ...;
. k=27: A153783;
. k=28: A195021;
. k=29: 0, 3, 35, 96, 186, 305, 453, 630, 836, 1071, 1335, 1628, ...;
. k=30: A153448;
. k=31: 0, 3, 37, 102, 198, 325, 483, 672, 892, 1143, 1425, 1738, ...;
. k=32: 0, 3, 38, 105, 204, 335, 498, 693, 920, 1179, 1470, 1793, ...;
. k=33: A153875.
Also:
a(n) - n         = A180223(n);
a(n) + n         = n*(11*n-3)/2 = 0, 4, 19, 45, 82, 130, 189, 259, ...;
a(n) - 2*n       = A051865(n);
a(n) + 2*n       = A022268(n);
a(n) - 3*n       = A152740(n-1);
a(n) + 3*n       = A022269(n);
a(n) - 4*n       = n*(11*n-13)/2 = 0, -1, 9, 30, 62, 105, 159, 224, ...;
a(n) + 4*n       = A254963(n);
a(n) - n*(n-1)/2 = A147874(n+1);
a(n) + n*(n-1)/2 = A094159(n) (case k=12);
a(n) - n*(n-1)   = A062741(n) (see above, this is the case k=9);
a(n) + n*(n-1)   = n*(13*n-7)/2 (case k=13);
a(n) - n*(n+1)/2 = A135706(n);
a(n) + n*(n+1)/2 = A033579(n);
a(n) - n*(n+1)   = A051682(n);
a(n) + n*(n+1)   = A186030(n);
a(n) - n^2       = A062708(n);
a(n) + n^2       = n*(13*n-5)/2 = 0, 4, 21, 51, 94, 150, 219, ..., etc.
Sum of reciprocals of a(n), for n > 0: 0.47118857003113149692081665034891...

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

Cf. sequences in Comments lines.
First differences are in A017425.
Cf. A033584, A180223.

Magma
```
[n*(11*n-5)/2: n in [0..50]];
```

I:=[0,3,17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..46]]; // Vincenzo Librandi, Aug 18 2013

Table[n (11 n - 5)/2, {n, 0, 50}]
CoefficientList[Series[x (3 + 8 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{3,-3,1},{0,3,17},50] (* Harvey P. Dale, Jan 14 2019 *)

a(n)=n*(11*n-5)/2 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: x*(3+8*x)/(1-x)^3.
a(n) + a(-n) = A033584(n).
From Elmo R. Oliveira, Dec 27 2024: (Start)
E.g.f.: exp(x)*x*(6 + 11*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = n + A180223(n). (End)

A152740 11 times triangular numbers.

Original entry on oeis.org

0, 11, 33, 66, 110, 165, 231, 308, 396, 495, 605, 726, 858, 1001, 1155, 1320, 1496, 1683, 1881, 2090, 2310, 2541, 2783, 3036, 3300, 3575, 3861, 4158, 4466, 4785, 5115, 5456, 5808, 6171, 6545, 6930, 7326, 7733, 8151, 8580, 9020, 9471, 9933, 10406, 10890, 11385, 11891

Offset: 0

Omar E. Pol, Dec 12 2008

Sequence found by reading the line from 0, in the direction 0, 11, ... and the same line from 0, in the direction 0, 33, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Axis perpendicular to A195149 in the same spiral. - Omar E. Pol, Sep 18 2011

Sum of the numbers from 5*n to 6*n. - Wesley Ivan Hurt, Dec 22 2015

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. A000217, A022268, A022269, A049598, A051865, A069125, A124080, A180223, A195149, A195313, A211013, A218530.

[11*n*(n+1)/2 : n in [0..60]]; // Wesley Ivan Hurt, Dec 22 2015

A152740:=n->11*n*(n+1)/2: seq(A152740(n), n=0..60); # Wesley Ivan Hurt, Dec 22 2015

Table[11*n*(n - 1)/2, {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 11, 33}, 100] (* G. C. Greubel, Dec 22 2015 *)

my(x='x+O('x^100)); concat(0, Vec(11*x/(1-x)^3)) \\ Altug Alkan, Dec 23 2015

a(n) = 11*n*(n+1)/2 = 11*A000217(n).
a(n) = a(n-1) + 11*n with n > 0, a(0)=0. - Vincenzo Librandi, Nov 26 2010
a(n) = A069125(n+1) - 1. - Omar E. Pol, Oct 03 2011
From Philippe Deléham, Mar 27 2013: (Start)
G.f.: 11*x/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=11, a(2)=33.
a(n) = A218530(11*n+10).
a(n) = A211013(n)+n = A022269(n)+5*n = A022268(n)+6*n = A180223(n)+9*n = A051865(n)+10*n. (End)
a(n) = Sum_{i=5*n..6*n} i. - Wesley Ivan Hurt, Dec 22 2015
From Amiram Eldar, Feb 21 2023: (Start)
Sum_{n>=1} 1/a(n) = 2/11.
Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/11.
Product_{n>=1} (1 - 1/a(n)) = -(11/(2*Pi))*cos(sqrt(19/11)*Pi/2).
Product_{n>=1} (1 + 1/a(n)) = (11/(2*Pi))*cos(sqrt(3/11)*Pi/2). (End)
E.g.f.: 11*exp(x)*x*(2 + x)/2. - Elmo R. Oliveira, Dec 25 2024

A211013 Second 13-gonal numbers: a(n) = n(11n+9)/2.

Original entry on oeis.org

0, 10, 31, 63, 106, 160, 225, 301, 388, 486, 595, 715, 846, 988, 1141, 1305, 1480, 1666, 1863, 2071, 2290, 2520, 2761, 3013, 3276, 3550, 3835, 4131, 4438, 4756, 5085, 5425, 5776, 6138, 6511, 6895, 7290, 7696, 8113, 8541, 8980, 9430, 9891, 10363

Offset: 0

Omar E. Pol, Aug 04 2012

Sequence found by reading the line from 0, in the direction 0, 31... and the line from 10, in the direction 10, 63,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313.

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

Bisection of A195313.
Second k-gonal numbers (k=5..14): A005449, A014105, A147875, A045944, A179986, A033954, A062728, A135705, this sequence, A211014.
Cf. A051865.

List([0..50], n-> n*(11*n+9)/2); # G. C. Greubel, Jul 04 2019

[n*(11*n+9)/2: n in [0..50]]; // G. C. Greubel, Jul 04 2019

Table[n*(11*n+9)/2, {n,0,50}] (* G. C. Greubel, Jul 04 2019 *)

a(n)=n*(11*n+9)/2 \\ Charles R Greathouse IV, Jun 17 2017

[n*(11*n+9)/2 for n in (0..50)] # G. C. Greubel, Jul 04 2019

G.f.: x*(10+x)/(1-x)^3. - Philippe Deléham, Mar 27 2013
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 0, a(1) = 10, a(2) = 31. - Philippe Deléham, Mar 27 2013
a(n) = A051865(n) + 9n = A180223(n) + 8n = A022268(n) + 5n = A022269(n) + 4n = A152740(n) - n. - Philippe Deléham, Mar 27 2013
a(n) = A218530(11n+9). - Philippe Deléham, Mar 27 2013
E.g.f.: x*(20 + 11*x)*exp(x)/2. - G. C. Greubel, Jul 04 2019

A241016 Triangle read by rows: T(n, k) = sum of k-th row of n X n square filled with the numbers 1 through n^2 reading across rows left-to-right.

Original entry on oeis.org

1, 3, 7, 6, 15, 24, 10, 26, 42, 58, 15, 40, 65, 90, 115, 21, 57, 93, 129, 165, 201, 28, 77, 126, 175, 224, 273, 322, 36, 100, 164, 228, 292, 356, 420, 484, 45, 126, 207, 288, 369, 450, 531, 612, 693, 55, 155, 255, 355, 455, 555, 655, 755, 855, 955, 66, 187, 308, 429, 550

Offset: 1

Kival Ngaokrajang, Aug 08 2014

See illustration in links.

The corresponding triangle with column sums is found in A251630. - Wolfdieter Lang, Dec 09 2014

			The triangle T(n, k) begins:
n\k  1   2   3   4   5   6   7   8   9  10 ...
1:   1
2:   3   7
3:   6  15  24
4:  10  26  42  58
5:  15  40  65  90 115
6:  21  57  93 129 165 201
7:  28  77 126 175 224 273 322
8:  36 100 164 228 292 356 420 484
9:  45 126 207 288 369 450 531 612 693
10: 55 155 255 355 455 555 655 755 855 955
... reformatted - _Wolfdieter Lang_, Dec 08 2014

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Kival Ngaokrajang, Illustration of initial terms

Columns k=1..6: A000217, A005449, A005475, A022265, A022267, A022269.
Diagonals: A081436, A059270, ...
Row sums: A037270.

Table[Sum[n*(k - 1) + j, {j,1,n}], {n,1,10}, {k,1,n}] // Flatten (* G. C. Greubel, Aug 23 2017 *)

trg(nn) = {for (n=1, nn, mm = matrix(n, n, i, j, j + n*(i-1)); for (i=1, n, print1(sum(j=1, n, mm[i, j]), ", ");); print(););} \\ Michel Marcus, Sep 15 2014

T(n, k) = Sum_{j=1..n} (n*(k-1)+ j), for n >= k >= 1. See the Michel Marcus program. - Wolfdieter Lang, Dec 08 2014

T(n, k) = binomial(n+1, 2) + n^2*(k-1). - Wolfdieter Lang, Dec 09 2014

Edited. - Wolfdieter Lang, Dec 08 2014

A218530 Partial sums of floor(n/11).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 171

Offset: 0

Philippe Deléham, Mar 27 2013

Apart from the initial zeros, the same as A008729.

			As square array:
..0....0....0....0....0....0....0....0....0....0....0
..1....2....3....4....5....6....7....8....9...10...11
.13...15...17...19...21...23...25...27...29...31...33
.36...39...42...45...48...51...54...57...60...63...66
.70...74...78...82...86...90...94...98..102..106..110
115..120..125..130..135..140..145..150..155..160..165
171..177..183..189..195..201..207..213..219..225..231
238..245..252..259..266..273..280..287..294..301..308
316..324..332..340..348..356..364..372..380..388..396
405..414..423..432..441..450..459..468..477..486..495
505..515..525..535..545..555..565..575..585..595..605
...

Cf. similar sequences: A000217, A002820, A130518, A130519, A130520, A174709, A174738, A118729, A218470, A131242.

a(11n)    = A051865(n).
a(11n+1)  = A180223(n).
a(11n+4)  = A022268(n).
a(11n+5)  = A022269(n).
a(11n+6)  = A254963(n)
a(11n+9)  = A211013(n).
a(11n+10) = A152740(n).
G.f.: x^11/((1-x)^2*(1-x^11)).

A008729 Molien series for 3-dimensional group [2, n] = *22n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 171, 177, 183, 189, 195, 201, 207, 213, 219

Offset: 0

N. J. A. Sloane

			..1....2....3....4....5....6....7....8....9...10...11
.13...15...17...19...21...23...25...27...29...31...33
.36...39...42...45...48...51...54...57...60...63...66
.70...74...78...82...86...90...94...98..102..106..110
115..120..125..130..135..140..145..150..155..160..165
171..177..183..189..195..201..207..213..219..225..231
238..245..252..259..266..273..280..287..294..301..308
316..324..332..340..348..356..364..372..380..388..396
405..414..423..432..441..450..459..468..477..486..495
505..515..525..535..545..555..565..575..585..595..605
...
The first six columns are A051865, A180223, A022268, A022269, A211013, A152740.
- _Philippe Deléham_, Apr 03 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 194
Index entries for Molien series
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,1,-2,1).

Cf. A001840, A001972, A008724-A008728, A008732, A218530.

a:=[1,2,3,4,5,6,7,8,9,10,11,13,15];; for n in [14..70] do a[n]:=2*a[n-1]-a[n-2]+a[n-11]-2*a[n-12]+a[n-13]; od; a; # G. C. Greubel, Jul 30 2019

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^11)) )); // G. C. Greubel, Jul 30 2019

g:= 1/((1-x)^2*(1-x^11)); gser:= series(g, x=0,72); seq(coeff(gser, x, n), n=0..70); # modified by G. C. Greubel, Jul 30 2019

CoefficientList[Series[1/((1-x)^2*(1-x^11)), {x,0,70}], x] (* Vincenzo Librandi, Jun 11 2013 *)

my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^11))) \\ G. C. Greubel, Jul 30 2019

(1/((1-x)^2*(1-x^11))).series(x, 70).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

From Mitch Harris, Sep 08 2008: (Start)
a(n) = Sum_{j=0..n+11} floor(j/11).
a(n-11) = (1/2)*floor(n/11)*(2*n - 9 - 11*floor(n/11)). (End)
a(n) = A218530(n+11). - Philippe Deléham, Apr 03 2013
From Chai Wah Wu, Jul 08 2016: (Start)
a(n) = 2*a(n-1) - a(n-2) + a(n-11) - 2*a(n-12) + a(n-13) for n > 12.
G.f.: 1/(1 - 2*x + x^2 - x^11 + 2*x^12 - x^13) = 1/((1-x)^3 *(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)). (End)

More terms from Vladimir Joseph Stephan Orlovsky, Mar 14 2010

cp's OEIS Frontend

A026817 Duplicate of A022269.

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A022289 a(n) = n*(31*n + 1)/2.

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A110449 Triangle read by rows: T(n,k) = n*((2*k+1)*n+1)/2, 0<=k<=n.

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A254963 a(n) = n*(11*n + 3)/2.

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Maxima

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A226492 a(n) = n*(11*n-5)/2.

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A152740 11 times triangular numbers.

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A211013 Second 13-gonal numbers: a(n) = n*(11*n+9)/2.

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A022289 a(n) = n(31n + 1)/2.

A110449 Triangle read by rows: T(n,k) = n((2k+1)*n+1)/2, 0<=k<=n.

A254963 a(n) = n(11n + 3)/2.

A226492 a(n) = n(11n-5)/2.

A211013 Second 13-gonal numbers: a(n) = n(11n+9)/2.