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 1-3 of 3 results.

A091493 Row sums of triangle A091492.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 21, 26, 32, 40, 49, 62, 75, 93, 113, 140, 170, 209, 255, 313, 383, 468, 567, 693, 840, 1022, 1235, 1503, 1816, 2209, 2667, 3248, 3923, 4754, 5743, 6949, 8384, 10126, 12195, 14717, 17726, 21369, 25732, 31020, 37393
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Crossrefs

Cf. A091492, A091497.

A091497 Number of nonzero terms in the n-th row of triangle A091492.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Crossrefs

Cf. A091492, A091493. Different from A087817 and A087836.

A091498 The sixth column of triangle A091492, excluding leading zeros.

Original entry on oeis.org

1, 2, 3, 5, 8, 11, 17, 23, 31, 41, 54, 68, 88, 109, 135, 165, 202, 241, 291, 344, 407, 477, 559, 646, 751, 862, 990, 1129, 1288, 1456, 1651, 1857, 2089, 2338, 2617, 2911, 3244, 3594, 3982, 4395, 4851, 5330, 5862, 6420, 7031, 7677, 8382, 9120, 9929, 10775
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Comments

Excluding leading zeros, columns k=3,4,5, of triangle A091492 list the partitions of n into k parts.
This sequence is related to the partitions of n into at most 6 parts (A001402) since A(x)=(1+x-x^5)*G001402(x), where G001402(x) is the g.f. for A001402.

Links

Crossrefs

Cf. A091492, A091493, A001402.

Programs

  • Mathematica
    CoefficientList[Series[(1+x-x^5)/((1-x)(1-x^2)(1-x^3)(1-x^4)(1-x^5)(1-x^6)),{x,0,60}],x] (* or *) LinearRecurrence[ {1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1},{1,2,3,5,8,11,17,23,31,41,54,68,88,109,135,165,202,241,291,344,407},60](* Harvey P. Dale, Dec 09 2012 *)
  • PARI
    {a(n)=polcoeff( (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)) +O(x^(n+1)),n,x)}

Formula

G.f.: (1+x-x^5)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6))
a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=8, a(5)=11, a(6)=17, a(7)=23, a(8)=31, a(9)=41, a(10)=54, a(11)=68, a(12)=88, a(13)=109, a(14)=135, a(15)=165, a(16)=202, a(17)=241, a(18)=291, a(19)=344, a(20)=407, a(n)=a(n-1)+ a(n-2)- a(n-5)-2*a(n-7)+a(n-9)+a(n-10)+a(n-11)+a(n-12)-2*a(n-14)-a(n-16)+ a(n-19)+ a(n-20)-a (n-21). - Harvey P. Dale, Dec 09 2012
Showing 1-3 of 3 results.

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

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