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 1-4 of 4 results.

A269428 Alternating sum of heptagonal pyramidal numbers.

Original entry on oeis.org

0, -1, 7, -19, 41, -74, 122, -186, 270, -375, 505, -661, 847, -1064, 1316, -1604, 1932, -2301, 2715, -3175, 3685, -4246, 4862, -5534, 6266, -7059, 7917, -8841, 9835, -10900, 12040, -13256, 14552, -15929, 17391, -18939, 20577, -22306, 24130, -26050, 28070
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Links

Crossrefs

Cf. A000292, A002413, A002717, A173196, A266677.

Programs

  • Magma
    [((20*n^3+42*n^2+4*n-9)*(-1)^n+9)/48: n in [0..50]]; // Vincenzo Librandi, Feb 26 2016
  • Mathematica
    Table[((20 n^3 + 42 n^2 + 4 n - 9) (-1)^n + 9)/48, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 7, -19, 41}, 41]
  • PARI
    a(n)=((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: x*(1 - 4*x)/((x - 1)*(x + 1)^4).
a(n) = ((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48.
a(n) = Sum_{k = 0..n} (-1)^k*A002413(k).
Sum_{n>=1} 1/a(n) = -0.8939139178060972723185724267951741... . - Vaclav Kotesovec, Feb 26 2016
E.g.f.: (9*sinh(x) - (33*x - 51*x^2 + 10*x^3)*exp(-x))/24. - Franck Maminirina Ramaharo, Nov 11 2018

A269429 Alternating sum of octagonal pyramidal numbers.

Original entry on oeis.org

0, -1, 8, -22, 48, -87, 144, -220, 320, -445, 600, -786, 1008, -1267, 1568, -1912, 2304, -2745, 3240, -3790, 4400, -5071, 5808, -6612, 7488, -8437, 9464, -10570, 11760, -13035, 14400, -15856, 17408, -19057, 20808, -22662, 24624, -26695, 28880, -31180, 33600
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Links

Crossrefs

Cf. A000292, A002414, A002717, A173196, A266677.

Programs

  • Mathematica
    Table[((2 n^3 + 4 n^2 - 1) (-1)^n + 1)/4, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 8, -22, 48}, 41]
  • PARI
    a(n)=(2*n^3 + 4*n^2 - 1)*(-1)^n\/4 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: x*(1 - 5*x)/((x - 1)*(x + 1)^4).
a(n) = ((2*n^3 + 4*n^2 - 1)*(-1)^n + 1)/4.
a(n) = Sum_{k = 0..n} (-1)^k*A002414(k).
Sum_{n>=1} 1/a(n) = -0.906890389180715042293808708467278316660747358... . - Vaclav Kotesovec, Feb 26 2016

A269440 Alternating sum of 9-gonal (or decagonal) pyramidal numbers.

Original entry on oeis.org

0, -1, 9, -25, 55, -100, 166, -254, 370, -515, 695, -911, 1169, -1470, 1820, -2220, 2676, -3189, 3765, -4405, 5115, -5896, 6754, -7690, 8710, -9815, 11011, -12299, 13685, -15170, 16760, -18456, 20264, -22185, 24225, -26385, 28671, -31084, 33630, -36310, 39130
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Links

Crossrefs

Cf. A000292, A002717, A007584, A173196, A266677.

Programs

  • Mathematica
    Table[(-1)^n (2 n - 1) ((14 n^2 + 34 n + 15)/48) + 5/16, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 9, -25, 55}, 41]

Formula

G.f.: x*(1 - 6*x)/((x - 1)*(x + 1)^4).
a(n) = (-1)^n*(2*n - 1)*(14*n^2 + 34*n + 15)/48 + 5/16.
a(n) = Sum_{k = 0..n} (-1)^k*A007584(k).

A269441 Alternating sum of 10-gonal (or decagonal) pyramidal numbers.

Original entry on oeis.org

0, -1, 10, -28, 62, -113, 188, -288, 420, -585, 790, -1036, 1330, -1673, 2072, -2528, 3048, -3633, 4290, -5020, 5830, -6721, 7700, -8768, 9932, -11193, 12558, -14028, 15610, -17305, 19120, -21056, 23120, -25313, 27642, -30108, 32718, -35473, 38380, -41440, 44660
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

Links

Crossrefs

Cf. A000292, A002717, A007585, A173196, A266677, A269428, A269429.

Programs

  • Magma
    [((-1)^n*(16*n^3+30*n^2-4*n-9)+9)/24: n in [0..40]]; // Vincenzo Librandi, Feb 27 2016
  • Mathematica
    Table[((-1)^n (16 n^3 + 30 n^2 - 4 n - 9) + 9)/24, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 10, -28, 62}, 41]

Formula

G.f.: x*(1 - 7*x)/((x - 1)*(x + 1)^4).
a(n) = ((-1)^n*(16*n^3 + 30*n^2 - 4*n - 9) + 9) /24.
a(n) = Sum_{k = 0..n} (-1)^k*A007585(k).
Sum_{n>=1} 1/a(n) = -0.9251958836055717745244669... . - Vaclav Kotesovec, Feb 26 2016
Showing 1-4 of 4 results.

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