cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A132770 a(n) = n*(n + 28).

Original entry on oeis.org

0, 29, 60, 93, 128, 165, 204, 245, 288, 333, 380, 429, 480, 533, 588, 645, 704, 765, 828, 893, 960, 1029, 1100, 1173, 1248, 1325, 1404, 1485, 1568, 1653, 1740, 1829, 1920, 2013, 2108, 2205, 2304, 2405, 2508, 2613, 2720, 2829, 2940, 3053, 3168, 3285, 3404, 3525
Offset: 0

Views

Author

Omar E. Pol, Aug 28 2007

Keywords

Links

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761.
Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769.

Programs

Formula

a(n) = 2*n + a(n-1) + 27, with a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)
G.f.: x*(29 - 27*x)/(1-x)^3. - Harvey P. Dale, Aug 03 2021
E.g.f.: x*(29 + x)*exp(x). - G. C. Greubel, Mar 13 2022

A132771 a(n) = n*(n + 29).

Original entry on oeis.org

0, 30, 62, 96, 132, 170, 210, 252, 296, 342, 390, 440, 492, 546, 602, 660, 720, 782, 846, 912, 980, 1050, 1122, 1196, 1272, 1350, 1430, 1512, 1596, 1682, 1770, 1860, 1952, 2046, 2142, 2240, 2340, 2442, 2546, 2652, 2760, 2870, 2982, 3096, 3212, 3330, 3450, 3572
Offset: 0

Views

Author

Omar E. Pol, Aug 28 2007

Keywords

Links

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.
Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.

Programs

Formula

a(n) = 2*n + a(n-1) + 28 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(29)/29 = A001008(29)/A102928(29) = 9227046511387/67543597321200, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/29 - 236266661971/9649085331600. (End)
From G. C. Greubel, Mar 13 2022: (Start)
G.f.: 2*(15*x - 14*x^2)/(1-x)^3.
E.g.f.: x*(30 + x)*exp(x). (End)

A132756 a(n) = n*(n + 27)/2.

Original entry on oeis.org

0, 14, 29, 45, 62, 80, 99, 119, 140, 162, 185, 209, 234, 260, 287, 315, 344, 374, 405, 437, 470, 504, 539, 575, 612, 650, 689, 729, 770, 812, 855, 899, 944, 990, 1037, 1085, 1134, 1184, 1235, 1287, 1340, 1394, 1449, 1505, 1562, 1620
Offset: 0

Views

Author

Omar E. Pol, Aug 28 2007

Keywords

Links

Crossrefs

Cf. A000217, A001008, A002805, A056126, A132769.

Programs

  • Mathematica
    Table[(n(n+27))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,14,29},50] (* Harvey P. Dale, Apr 10 2022 *)
  • PARI
    a(n)=n*(n+27)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

Let f(n,i,a) = Sum_{k=0..n-i} (binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j)), then a(n) = -f(n,n-1,14), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 13 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(n) = 14*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
From Chai Wah Wu, Jun 02 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: x*(13*x - 14)/(x - 1)^3. (End)
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=1} 1/a(n) = 2*A001008(27)/(27*A002805(27)) = 312536252003/1084231348200.
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/27 - 57128792093/1084231348200. (End)
From Elmo R. Oliveira, Jan 12 2025: (Start)
E.g.f.: exp(x)*x*(28 + x)/2.
a(n) = A132769(n)/2. (End)

A132772 a(n) = n*(n + 30).

Original entry on oeis.org

0, 31, 64, 99, 136, 175, 216, 259, 304, 351, 400, 451, 504, 559, 616, 675, 736, 799, 864, 931, 1000, 1071, 1144, 1219, 1296, 1375, 1456, 1539, 1624, 1711, 1800, 1891, 1984, 2079, 2176, 2275, 2376, 2479, 2584, 2691, 2800, 2911, 3024, 3139, 3256, 3375, 3496, 3619
Offset: 0

Views

Author

Omar E. Pol, Aug 28 2007

Keywords

Links

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566.
Cf. A028569, A067079, A098849, A098850, A098603, A098847, A098848, A102928, A120071.
Cf. A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767.
Cf. A132768, A132769, A132770, A132771.

Programs

Formula

G.f.: x*(31-29*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
a(0)=0, a(1)=31, a(2)=64, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 06 2015
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)
E.g.f.: x*(31 + x)*exp(x). - G. C. Greubel, Mar 13 2022

A132773 a(n) = n*(n + 31).

Original entry on oeis.org

0, 32, 66, 102, 140, 180, 222, 266, 312, 360, 410, 462, 516, 572, 630, 690, 752, 816, 882, 950, 1020, 1092, 1166, 1242, 1320, 1400, 1482, 1566, 1652, 1740, 1830, 1922, 2016, 2112, 2210, 2310, 2412, 2516, 2622, 2730, 2840, 2952, 3066, 3182, 3300, 3420, 3542, 3666
Offset: 0

Views

Author

Omar E. Pol, Aug 28 2007

Keywords

Links

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132758, A132759, A132760.
Cf. A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.
Cf. A132771, A132772.

Programs

Formula

G.f.: 2*x*(-16+15*x)/(-1+x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*A132758(n). - R. J. Mathar, Jul 22 2009
a(n) = 2*n + a(n-1) + 30, with n > 0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(31)/31 = A001008(31)/A102928(31) = 290774257297357/2238255069850800, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/31 - 7313175618421/319750724264400. (End)
From Elmo R. Oliveira, Dec 13 2024: (Start)
E.g.f.: exp(x)*x*(32 + x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Showing 1-5 of 5 results.

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