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 1-2 of 2 results.

A044102 Multiples of 36.

Original entry on oeis.org

0, 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728
Offset: 0

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Author

Keywords

Comments

Also, k such that Fibonacci(k) mod 27 = 0. - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 18 2004
A033183(a(n)) = n+1. - Reinhard Zumkeller, Nov 07 2009
A122841(a(n)) > 1 for n > 0. - Reinhard Zumkeller, Nov 10 2013
Sum of the numbers from 4*(n-1) to 4*(n+1). - Bruno Berselli, Oct 25 2018

Crossrefs

Programs

Formula

G.f.: 36*x/(1 - x)^2.
a(n) = A167632(n+1). - Reinhard Zumkeller, Nov 07 2009
a(n) = 36*n. - Vincenzo Librandi, Jan 26 2011
From Elmo R. Oliveira, Apr 10 2025: (Start)
E.g.f.: 36*x*exp(x).
a(n) = 18*A005843(n) = 2*A008600(n).
a(n) = 2*a(n-1) - a(n-2). (End)

A033183 a(n) = number of pairs (p,q) such that 4*p + 9*q = n.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2
Offset: 0

Views

Author

Michel Tixier (tixier(AT)dyadel.net)

Keywords

Comments

From Reinhard Zumkeller, Nov 07 2009: (Start)
In other words: number of partitions into 4 or 9;
a(n) <= A078134(n); a(A078135(n)) = 0;
a(A167632(n)) = n and a(m) < n for m < A167632(n). (End)

Crossrefs

Cf. A033182.

Programs

  • Mathematica
    CoefficientList[Series[1/((1-x^4)(1-x^9)),{x,0,80}],x] (* or  *) LinearRecurrence[{0,0,0,1,0,0,0,0,1,0,0,0,-1}, {1,0,0,0,1,0,0,0,1,1,0,0,1}, 80] (* Harvey P. Dale, Oct 13 2012 *)

Formula

a(n) = [ 7 n/9 ]+1+[ -3 n/4 ].
G.f.: 1/((1-x^4)*(1-x^9)). - Vladeta Jovovic, Nov 12 2004
a(n) = a(n-4) + a(n-9) - a(n-13). - R. J. Mathar, Dec 04 2011
Showing 1-2 of 2 results.