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.

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A101861 n*(n+5)*(50+45*n+n^2)/24.

Original entry on oeis.org

24, 84, 194, 369, 625, 979, 1449, 2054, 2814, 3750, 4884, 6239, 7839, 9709, 11875, 14364, 17204, 20424, 24054, 28125, 32669, 37719, 43309, 49474, 56250, 63674, 71784, 80619, 90219, 100625, 111879, 124024, 137104, 151164, 166250, 182409
Offset: 1

Views

Author

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004

Keywords

Comments

Essentially the partial sums of A101860.
5th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 4: 1,11,11,1: 5th row of the array in the examples of A101860.

Links

Formula

G.f. x*(x-2)*(x^2-12*x+12) / (x-1)^5 . - R. J. Mathar, Dec 06 2011

A101862 a(n) = n*(n+1)*(n+7)*(122+57*n+n^2)/120.

Original entry on oeis.org

24, 108, 302, 671, 1296, 2275, 3724, 5778, 8592, 12342, 17226, 23465, 31304, 41013, 52888, 67252, 84456, 104880, 128934, 157059, 189728, 227447, 270756, 320230, 376480, 440154, 511938, 592557, 682776, 783401, 895280, 1019304, 1156408, 1307572, 1473822, 1656231
Offset: 1

Views

Author

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004

Keywords

Comments

Partial sums of A101861.
6th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 4: 1,11,11,1: 6th row of the array in the examples of A101860.

Links

Crossrefs

Cf. A101860, A101861.

Programs

  • Magma
    [n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120 : n in [1..50]]; // Wesley Ivan Hurt, Dec 06 2016
  • Maple
    A101862:=n->n*(n+1)*(n+7)*(122+57*n+n^2)/120: seq(A101862(n), n=1..50); # Wesley Ivan Hurt, Dec 06 2016
  • Mathematica
    Table[n*(n + 1)*(n + 7)*(122 + 57*n + n^2)/120, {n, 50}] (* Wesley Ivan Hurt, Dec 06 2016 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{24,108,302,671,1296,2275},50] (* Harvey P. Dale, Oct 15 2020 *)

Formula

G.f.: x*(2-x)*(x^2-12*x+12) / (1-x)^6. - R. J. Mathar, Dec 06 2011
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 6. - Wesley Ivan Hurt, Dec 06 2016
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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