A177100 -id:A177100 - cp's OEIS frontend

A177116 Partial sums of round(n^2/11).

0, 0, 0, 1, 2, 4, 7, 11, 17, 24, 33, 44, 57, 72, 90, 110, 133, 159, 188, 221, 257, 297, 341, 389, 441, 498, 559, 625, 696, 772, 854, 941, 1034, 1133, 1238, 1349, 1467, 1591, 1722, 1860, 2005, 2158, 2318, 2486, 2662, 2846, 3038, 3239, 3448, 3666, 3893

Offset: 0

Mircea Merca, Dec 09 2010

The round function, also called the nearest integer function, is defined here by round(x)=floor(x+1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(11) = 0 + 0 + 0 + 1 + 1 + 2 + 3 + 4 + 6 + 7 + 9 + 11 = 44.

Vincenzo Librandi, Table of n, a(n) for n = 0..870
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A173690 (k=5), A173691 (k=6), A173722 (k=8), A177100 (k=9), A181120 (k=12).

seq(round((2*n^3+3*n^2-11*n)/66),n=0..50)

Accumulate[Round[Range[0,50]^2/11]] (* or *) LinearRecurrence[{3,-3,1,0,0,0,0,0,0,0,1,-3,3,-1},{0,0,0,1,2,4,7,11,17,24,33,44,57,72},60] (* Harvey P. Dale, Dec 10 2014 *)

a(n)=(2*n^3+3*n^2-11*n+18)\66 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = round((n-2)*(n+3)*(2*n+1)/66).
a(n) = floor((2*n^3 + 3*n^2 - 11*n + 18)/66).
a(n) = ceiling((2*n^3 + 3*n^2 - 11*n - 30)/66).
a(n) = round(n*(2*n^2 + 3*n - 11)/66).
a(n) = a(n-11) + (n+1)*(n-11) + 44, n > 10.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14). - R. J. Mathar, Dec 10 2010
G.f.: x^3 *(1+x) *(x^2-x+1) *(x^4-x^3+x^2-x+1) / ( (x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) *(x-1)^4 ). - R. J. Mathar, Dec 10 2010 [Typo fixed by Colin Barker, Oct 10 2012]

A177176 Partial sums of round(n^2/13).

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 7, 11, 16, 22, 30, 39, 50, 63, 78, 95, 115, 137, 162, 190, 221, 255, 292, 333, 377, 425, 477, 533, 593, 658, 727, 801, 880, 964, 1053, 1147, 1247, 1352, 1463, 1580, 1703, 1832, 1968, 2110, 2259, 2415, 2578, 2748, 2925, 3110, 3302

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

			a(13) = 0 + 0 + 0 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 11 + 13 = 63.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116, A181120.

[Round(n*(n+1)*(2*n+1)/78): n in [0..60]]; // Vincenzo Librandi, Jun 23 2011

Maple
```
seq(round(n*(n+1)*(2*n+1)/78),n=0..50)
```
PARI
```
s=0;vector(90,n,s+=n^2\13)
```

a(n) = round(n*(n+1)*(2*n+1)/78).
a(n) = floor((n+3)*(2*n^2 - 3*n + 10)/78).
a(n) = ceiling((n-2)*(2*n^2 + 7*n + 15)/78).
a(n) = a(n-13) + (n+1)*(n-13) + 63, n > 12.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-13) - 3*a(n-14) + 3*a(n-15) - a(n-16) with g.f. x^3*(1+x)*(x^2 - x + 1)*(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1) / ( (x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4 ). - R. J. Mathar, Dec 13 2010

A177189 Partial sums of round(n^2/16).

Original entry on oeis.org

0, 0, 0, 1, 2, 4, 6, 9, 13, 18, 24, 32, 41, 52, 64, 78, 94, 112, 132, 155, 180, 208, 238, 271, 307, 346, 388, 434, 483, 536, 592, 652, 716, 784, 856, 933, 1014, 1100, 1190, 1285, 1385, 1490, 1600, 1716, 1837, 1964, 2096, 2234, 2378, 2528, 2684

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(16) = 0 + 0 + 0 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 11 + 12 + 14 + 16 = 94.

Vincenzo Librandi, Table of n, a(n) for n = 0..885
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Floor((n+3)*(2*n^2-3*n+13)/96): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

seq(round((2*n^3+3*n^2+4*n)/96),n=0..50)

Accumulate[Round[Range[0,50]^2/16]]  (* Harvey P. Dale, Mar 16 2011 *)

a(n) = round((2*n+1)*(2*n^2 + 2*n + 3)/192).
a(n) = floor((n+3)*(2*n^2 - 3*n + 13)/96).
a(n) = ceiling((n-2)*(2*n^2 + 7*n + 18)/96).
a(n) = round((2*n^3 + 3*n^2 + 4*n)/96).
a(n) = a(n-16) + (n+1)*(n-16) + 94, n > 15.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11) with g.f. x^3*(1 - x + x^2 + x^4 - x^3) / ( (1+x)*(1+x^2)*(1+x^4)*(x-1)^4 ). - R. J. Mathar, Dec 13 2010

A177205 Partial sums of round(n^2/17).

Original entry on oeis.org

0, 0, 0, 1, 2, 3, 5, 8, 12, 17, 23, 30, 38, 48, 60, 73, 88, 105, 124, 145, 169, 195, 223, 254, 288, 325, 365, 408, 454, 503, 556, 613, 673, 737, 805, 877, 953, 1034, 1119, 1208, 1302, 1401, 1505, 1614, 1728, 1847, 1971, 2101, 2237, 2378, 2525

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x)=floor(x+1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(17) = 0 + 0 + 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 13 + 15 + 17 = 105.

Vincenzo Librandi, Table of n, a(n) for n = 0..890
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Floor((2*n^3+3*n^2+n+36)/102): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

Maple
```
seq(round(n*(n+1)*(2*n+1)/102),n=0..50)
```

Accumulate[Round[Range[0,50]^2/17]] (* Harvey P. Dale, Jul 04 2022 *)

a(n) = round(n*(n+1)*(2*n+1)/102).
a(n) = floor((2*n^3 + 3*n^2 + n + 36)/102).
a(n) = ceiling((2*n^3 + 3*n^2 + n - 36)/102).
a(n) = a(n-17) + (n+1)*(n-17) + 105, n > 16.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-17) - 3*a(n-18) + 3*a(n-19) - a(n-20) with g.f. x^3 *(1+x) *(x^12 - 2*x^11 + 2*x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + 2*x^2 - 2*x + 1) / ( (x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) *(x-1)^4 ). - R. J. Mathar, Dec 13 2010

A177237 Partial sums of round(n^2/19).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 4, 7, 10, 14, 19, 25, 33, 42, 52, 64, 77, 92, 109, 128, 149, 172, 197, 225, 255, 288, 324, 362, 403, 447, 494, 545, 599, 656, 717, 781, 849, 921, 997, 1077, 1161, 1249, 1342, 1439, 1541, 1648, 1759, 1875, 1996, 2122, 2254

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(19) = 0 + 0 + 0 + 0 + 1 + 1 + 2 + 3 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 13 + 15 + 17 + 19 = 128.

Vincenzo Librandi, Table of n, a(n) for n = 0..895
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Floor((2*n^3+3*n^2-11*n+42)/114): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

seq(round((2*n^3+3*n^2-11*n)/114),n=0..50)

Accumulate[Round[Range[0,50]^2/19]] (* Harvey P. Dale, Aug 15 2022 *)

[(2*n^3 +3*n^2 -11*n +42)//114 for n in range(61)] # G. C. Greubel, Apr 27 2024

a(n) = round((n-2)*(n+3)*(2*n+1)/114).
a(n) = floor((2*n^3 + 3*n^2 - 11*n + 42)/114).
a(n) = ceiling((2*n^3 + 3*n^2 - 11*n - 54)/114).
a(n) = round((2*n^3 + 3*n^2 - 11*n)/114).
a(n) = a(n-19) + (n+1)*(n-19) + 128, n > 18.
From R. J. Mathar, Dec 13 2010: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-19) - 3*a(n-20) + 3*a(n-21) - a(n-22).
G.f.: x^4*(1+x)*(1 - x + x^2 - x^3 + x^4)*(1 - x + x^2 - x^4 + x^6 - x^7 + x^8)/((1-x)^3 * (1 - x^19)). (End)

A177239 Partial sums of round(n^2/20).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 49, 60, 73, 87, 103, 121, 141, 163, 187, 213, 242, 273, 307, 343, 382, 424, 469, 517, 568, 622, 680, 741, 806, 874, 946, 1022, 1102, 1186, 1274, 1366, 1463, 1564, 1670, 1780, 1895, 2015, 2140

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(20) = 0 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 11 + 13 + 14 + 16 + 18 + 20 = 141.

Vincenzo Librandi, Table of n, a(n) for n = 0..895
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,1,-2,0,2,-1).

Cf. A001304, A177100, A177116.

[Floor((n+4)*(2*n^2-5*n+6)/120): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

Maple
```
seq(round(n*(n-2)*(2*n+7)/120),n=0..50)
```

f[n_] := Round[n^2/20]; Accumulate@ Array[f, 51, 0] (* Robert G. Wilson v, Dec 20 2010 *)

[(n+4)*(2*n^2 -5*n +6)//120 for n in range(56)] # G. C. Greubel, Apr 27 2024

a(n) = A001304(n-4).
a(n) = round((2*n+1)*(2*n^2 + 2*n - 15)/240).
a(n) = floor((n+4)*(2*n^2 - 5*n + 6)/120).
a(n) = ceiling((n-3)*(2*n^2 + 9*n + 13)120).
a(n) = round(n*(n-2)*(2*n+7)/120).
a(n) = a(n-20) + (n+1)*(n-20) + 141, n > 19.
From R. J. Mathar, Dec 12 2010: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9).
G.f.: x^4 / ( (1+x)*(1+x+x^2+x^3+x^4)*(1-x)^4 ). (End)

A177277 Partial sums of round(n^2/28).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 3, 5, 7, 10, 14, 18, 23, 29, 36, 44, 53, 63, 75, 88, 102, 118, 135, 154, 175, 197, 221, 247, 275, 305, 337, 371, 408, 447, 488, 532, 578, 627, 679, 733, 790, 850, 913, 979, 1048, 1120, 1196, 1275, 1357, 1443, 1532

Offset: 0

Mircea Merca, Dec 10 2010

The round function, also called the nearest integer function, is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(28) = 0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 13 + 14 + 16 + 17 + 19 + 21 + 22 + 24 + 26 + 28 = 275.

Vincenzo Librandi, Table of n, a(n) for n = 0..905
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Floor((n+4)*(2*n^2-5*n+18)/168): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

Maple
```
seq(round(n*(n+2)*(2*n-1)/168),n=0..50)
```

Accumulate[Floor[Range[0,50]^2/28+1/2]] (* Harvey P. Dale, Feb 02 2012 *)

a(n) = round((2*n+1)*(2*n^2 + 2*n - 3)/336).
a(n) = floor((n+4)*(2*n^2 - 5*n + 18)/168).
a(n) = ceiling((n-3)*(2*n^2 + 9*n + 25)/168).
a(n) = round(n*(n+2)*(2*n-1)/168).
a(n) = a(n-28) + (n+1)*(n-28) + 275, n > 27.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-14) - 3*a(n-15) + 3*a(n-16) - a(n-17) with g.f. x^4*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8) / ( (1+x)*(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x-1)^4 ). - R. J. Mathar, Dec 12 2010

A177332 Partial sums of round(n^2/29).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 3, 5, 7, 10, 13, 17, 22, 28, 35, 43, 52, 62, 73, 85, 99, 114, 131, 149, 169, 191, 214, 239, 266, 295, 326, 359, 394, 432, 472, 514, 559, 606, 656, 708, 763, 821, 882, 946, 1013, 1083, 1156, 1232, 1311, 1394, 1480

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(17) = 0 + 0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 62.

Vincenzo Librandi, Table of n, a(n) for n = 0..905
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A177100, A177116.

[Floor((n+4)*(2*n^2-5*n+21)/174): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

Maple
```
seq(round(n*(n+1)*(2*n+1)/174),n=0..50)
```

Accumulate[Table[Round[n^2/29],{n,0,60}]] (* Harvey P. Dale, Dec 18 2010 *)

a(n)=(2*n^3+3*n^2+n+84)\174 \\ Charles R Greathouse IV, Apr 06 2012

def A177332(n): return (n*(n*(2*n + 3) + 1) + 84)//174 # Chai Wah Wu, Jan 31 2023

a(n) = round(n*(n+1)*(2*n+1)/174).
a(n) = floor((n+4)*(2*n^2 - 5*n + 21)/174).
a(n) = ceiling((n-3)*(2*n^2 + 9*n + 28)/174).
a(n) = a(n-29) + (n+1)*(n-29) + 266, n > 28.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-29) - 3*a(n-30) + 3*a(n-31) - a(n-32). - R. J. Mathar, Dec 13 2010
G.f.: x^4*(x+1)*(x^2 - x + 1)*(x^4 - x^2 + 1)*(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)*(x^10 - x^6 + x^5 - x^4 + 1)/((x-1)^4*(x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)). - Colin Barker, Apr 06 2012

A177337 Partial sums of round(n^2/36).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 40, 48, 57, 67, 78, 90, 103, 118, 134, 151, 170, 190, 212, 235, 260, 287, 315, 345, 377, 411, 447, 485, 525, 567, 611, 658, 707, 758, 812, 868, 927, 988, 1052, 1119, 1188

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

			a(19) = 0 + 0 + 0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 5 + 5 + 6 + 7 + 8 + 9 + 10 = 67.

Vincenzo Librandi, Table of n, a(n) for n = 0..910
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Floor((n+5)*(2*n^2-7*n+17)/216): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

seq(round((2*n^3+3*n^2-18*n)/216),n=0..50)

Accumulate[Floor[Range[0,60]^2/36+1/2]] (* Harvey P. Dale, Sep 29 2011 *)

a(n) = round((2*n+1)*(2*n^2 + 2*n - 19)/432).
a(n) = floor((n+5)*(2*n^2 - 7*n + 17)/216).
a(n) = ceiling((n-4)*(2*n^2 + 11*n + 26)/216).
a(n) = round((2*n^3 + 3*n^2 - 18*n)/216).
a(n) = a(n-36) + (n+1)*(n-36) + 447, n > 35.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-18) - 3*a(n-19) + 3*a(n-20) - a(n-21) with g.f. x^5*(1 - x + x^3 - x^4 + x^5 - x^6 + x^7 - x^9 + x^10) / ( (1+x) *(1 + x + x^2) *(x^2 - x + 1) *(x^6 + x^3 + 1) *(x^6 - x^3 + 1) *(x-1)^4 ). - R. J. Mathar, Dec 13 2010

A177339 Partial sums of round(n^2/44).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 8, 11, 14, 18, 22, 27, 33, 40, 47, 55, 64, 74, 85, 97, 110, 124, 139, 156, 174, 193, 213, 235, 258, 283, 309, 337, 366, 397, 430, 465, 501, 539, 579, 621, 665, 711, 759, 809, 861, 916, 973

Offset: 0

Mircea Merca, Dec 10 2010

The round function is defined here by round(x) = floor(x + 1/2).

There are several sequences of integers of the form round(n^2/k) for whose partial sums we can establish identities as following (only for k = 2, ..., 9, 11, 12, 13, 16, 17, 19, 20, 28, 29, 36, 44).

			a(15) = 0 + 0 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 3 + 3 + 4 + 4 + 5 = 27.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Cf. A177100, A177116.

[Round((2*n+1)*(2*n^2+2*n-15)/528): n in [0..60]]; // Vincenzo Librandi, Jun 23 2011

Maple
```
seq(round(n*(n-2)*(2*n+7)/264),n=0..50)
```

a(n) = round((2*n+1)*(2*n^2 + 2*n - 15)/528).
a(n) = floor((n+5)*(2*n^2 - 7*n + 21)/264).
a(n) = ceiling((n-4)*(2*n^2 + 11*n + 30)/264).
a(n) = round(n*(n-2)*(2*n+7)/264).
a(n) = a(n-44) + (n+1)*(n-44) + 665, n > 43.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-11) - 2*a(n-12) + 2*a(n-14) - a(n-15) with g.f. x^5*(1 - x^2 + x^4) / ( (1+x) *(x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) *(x-1)^4 ). - R. J. Mathar, Dec 13 2010

cp's OEIS Frontend

A177116 Partial sums of round(n^2/11).

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A177176 Partial sums of round(n^2/13).

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A177189 Partial sums of round(n^2/16).

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A177205 Partial sums of round(n^2/17).

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A177237 Partial sums of round(n^2/19).

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A177239 Partial sums of round(n^2/20).

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