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.

User: Katherine Guo

Katherine Guo's wiki page.

Katherine Guo has authored 3 sequences.

A239831 Floor(7n^2/2) + floor(5n/2) + floor(3n/7).

Original entry on oeis.org

5, 19, 39, 67, 101, 143, 191, 247, 308, 379, 454, 539, 628, 727, 830, 942, 1060, 1186, 1318, 1458, 1604, 1758, 1917, 2086, 2259, 2442, 2629, 2826, 3027, 3237, 3453, 3677, 3907, 4145, 4389, 4641, 4898, 5165, 5436, 5717, 6002, 6297, 6596, 6904, 7218, 7540
Offset: 1

Views

Author

Katherine Guo, Mar 27 2014

Keywords

Comments

This is a quadratic sequence.

Examples

			For n=3, a(3) = floor(7*3^2/2) + floor(5*3/2) + floor(3*3/7) = 39.

Links

Programs

  • Magma
    [Floor(7*n^2/2) + Floor(5*n/2) + Floor(3*n/7): n in [1..50]]; // Vincenzo Librandi, Mar 29 2014
  • Maple
    A239831:=n->floor(7*n^2/2) + floor(5*n/2) + floor(3*n/7); seq(A239831(n), n=1..50); # Wesley Ivan Hurt, Mar 28 2014
  • Mathematica
    Table[Floor[7 n^2/2] + Floor[5 n/2] + Floor[3 n/7], {n, 50}] (* Bruno Berselli, Mar 28 2014 *)

Formula

a(n) = (n(7n + 5) + (-1)^n - 1)/2 + A132270(3n + 1). [Bruno Berselli, Mar 28 2014]
a(n) = +a(n-1) +a(n-2) -a(n-3) +a(n-7) -a(n-8) -a(n-9) +a(n-10). [Bruno Berselli, Mar 28 2014]

Extensions

More terms from Bruno Berselli, Mar 28 2014

A239794 5*n^2 + 4*n - 15.

Original entry on oeis.org

-6, 13, 42, 81, 130, 189, 258, 337, 426, 525, 634, 753, 882, 1021, 1170, 1329, 1498, 1677, 1866, 2065, 2274, 2493, 2722, 2961, 3210, 3469, 3738, 4017, 4306, 4605, 4914, 5233, 5562, 5901, 6250, 6609, 6978, 7357, 7746, 8145, 8554, 8973, 9402, 9841, 10290
Offset: 1

Views

Author

Katherine Guo, Mar 26 2014

Keywords

Comments

Follows the integer values from 1 on the quadratic equation 5*x^2 + 4*n - 15, this is the case x=n.

Examples

			For n=3, a(3) = 5*3^2 + 4*3 - 15 = 42; for n=6, a(6) = 5*6^2 + 4*6 - 15 = 189.

Links

Crossrefs

Cf. A008590, A017377.

Programs

  • Magma
    [5*n^2+4*n-15: n in [1..50]];
  • Mathematica
    Table[5 n^2 + 4 n - 15, {n, 50}]
CoefficientList[Series[(6 - 31 x + 15 x^2)/(x - 1)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 29 2014 *)
LinearRecurrence[{3,-3,1},{-6,13,42},50] (* Harvey P. Dale, May 30 2025 *)
  • PARI
    a(n)=5*n^2+4*n-15 \\ Charles R Greathouse IV, Jun 17 2017

Formula

From Bruno Berselli, Mar 27 2014: (Start)
G.f.: -x*(6 - 31*x + 15*x^2)/(1 - x)^3.
a(n+1) - a(n) = A017377(n).
a(n) - a(-n) = A008590(n). (End)

A239796 a(n) = 7*n^2 + 2*n - 15.

Original entry on oeis.org

-6, 17, 54, 105, 170, 249, 342, 449, 570, 705, 854, 1017, 1194, 1385, 1590, 1809, 2042, 2289, 2550, 2825, 3114, 3417, 3734, 4065, 4410, 4769, 5142, 5529, 5930, 6345, 6774, 7217, 7674, 8145, 8630, 9129, 9642, 10169, 10710, 11265, 11834, 12417, 13014, 13625, 14250, 14889, 15542, 16209, 16890
Offset: 1

Views

Author

Katherine Guo, Mar 26 2014

Keywords

Comments

Follows the integer values from 1 on the parabola: 7*n^2 + 2*n - 15.
Real roots: (-1 +- sqrt(106))/7. - Wesley Ivan Hurt, Mar 26 2014
The first in the family of parabolas of the form: prime(k+3)*n^2 + prime(k)*n - prime(k+1)*prime(k+2), where k >= 1 (k=1 gives a(n)). - Wesley Ivan Hurt, Mar 26 2014

Examples

			For n=3, a(3) = 7*3^2 + 2*3 - 15 = 54; for n=6, a(6) = 7*6^2 + 2*6 - 15 = 249.

Links

Programs

Formula

a(n) = n * A017005(n) - 15. - Wesley Ivan Hurt, Mar 26 2014
G.f.: -x*(6 - 35*x + 15*x^2)/(1 - x)^3. - Bruno Berselli, Mar 27 2014

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