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.

A121136 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.

Original entry on oeis.org

1, 3, 13, 45, 164, 527, 1652, 4876, 14000, 38800, 105112, 278104, 722736, 1846320, 4650368, 11560320, 28413312, 69111168, 166551680, 397975680, 943672576, 2221821184, 5197313024, 12084884480, 27944656896, 64286203904, 147182565376
Offset: 4

Views

Author

N. J. A. Sloane, Aug 13 2006

Keywords

Links

Crossrefs

Cf. A121133. - R. J. Mathar, Aug 07 2008

Programs

  • Maple
    H := proc(r,alpha,q) local rhalf,alphahalf ; rhalf := floor(r/2) ; alphahalf := floor(alpha/2) ; (binomial(rhalf-1,alphahalf-1)*(q-3) +binomial(rhalf-1,alphahalf))*(q-3)^(rhalf-alphahalf-1) ; end: J := proc(r,alpha,q) (binomial(r-2,alpha-2)*(q-3)^2+2*binomial(r-2,alpha-1) *(q-3)+binomial(r-2,alpha))*(q-3)^(r-alpha-2) ; end: Ifunc := proc(r,alpha,q) J(r,alpha,q)/4+binomial(2,r-alpha)/4+ (1+(-1)^(r+alpha) +(1+(-1)^alpha)*(1-(-1)^r)/2)*H(r,alpha,q)/4 ; end: A121136 := proc(n) Ifunc(n,4,5) ; end: for n from 4 to 80 do printf("%d,",A121136(n)) ; od: # R. J. Mathar, Aug 07 2008
  • Mathematica
    Join[{1, 3, 13}, LinearRecurrence[{10, -34, 20, 148, -328, 8, 688, -640, -256, 640, -256}, {45, 164, 527, 1652, 4876, 14000, 38800, 105112, 278104, 722736, 1846320}, 24]] (* Jean-François Alcover, Mar 31 2020 *)

Formula

G.f.: x^4 * (64*x^13 -32*x^12 -192*x^11 +128*x^10 +212*x^9 -172*x^8 -114*x^7 +110*x^6 +41*x^5 -52*x^4 -3*x^3 +17*x^2 -7*x+1) / ((2*x-1)^5 * (2*x^2-1)^3). - Colin Barker, Nov 30 2012

Extensions

Extended beyond a(10) by R. J. Mathar, Aug 07 2008

A121135 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.

Original entry on oeis.org

1, 2, 8, 22, 74, 208, 598, 1600, 4248, 10880, 27512, 68096, 166528, 401408, 957728, 2260992, 5292672, 12288000, 28329344, 64880640, 147721216, 334495744, 753670656, 1690304512, 3774887936, 8396996608, 18610157568, 41104179200
Offset: 3

Views

Author

N. J. A. Sloane, Aug 13 2006

Keywords

Links

Crossrefs

Cf. A121133. - R. J. Mathar, Aug 07 2008

Programs

  • Maple
    H := proc(r,alpha,q) local rhalf,alphahalf ; rhalf := floor(r/2) ; alphahalf := floor(alpha/2) ; (binomial(rhalf-1,alphahalf-1)*(q-3)+binomial(rhalf-1,alphahalf))*(q-3)^(rhalf-alphahalf-1) ; end: J := proc(r,alpha,q) (binomial(r-2,alpha-2)*(q-3)^2+2*binomial(r-2,alpha-1)*(q-3)+binomial(r-2,alpha))*(q-3)^(r-alpha-2) ; end: Ifunc := proc(r,alpha,q) J(r,alpha,q)/4+binomial(2,r-alpha)/4+ (1+(-1)^(r+alpha)+(1+(-1)^alpha)*(1-(-1)^r)/2)*H(r,alpha,q)/4 ; end: A121135 := proc(n) Ifunc(n,3,5) ; end: for n from 3 to 80 do printf("%d,",A121135(n)) ; od: # R. J. Mathar, Aug 07 2008

Formula

G.f.: x^3 * (16*x^10-40*x^8+8*x^7+30*x^6-18*x^4-2*x^3+12*x^2-6*x+1) / ((2*x-1)^4 * (2*x^2-1)^2). - Colin Barker, Nov 30 2012

Extensions

Extended beyond a(10) by R. J. Mathar, Aug 07 2008

A120652 Triangle read by rows: numbers of isomers of unbranched a-4-catapolypentagons.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 5, 2, 1, 3, 8, 11, 8, 3, 1, 6, 16, 30, 22, 13, 3, 1, 10, 38, 72, 74, 45, 18, 4, 1, 20, 80, 182, 208, 164, 73, 25, 4, 1, 36, 180, 434, 598, 527, 310, 119, 32, 5, 1, 72, 384, 1048, 1600, 1652, 1120, 548, 172, 41, 5, 1
Offset: 0

Views

Author

N. J. A. Sloane, Aug 18 2006

Keywords

Examples

			Triangle begins
1
1 1
1 1 1
1 2 2 1
2 3 5 2 1
3 8 11 8 3 1
6 16 30 22 13 3 1

References

  • J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.

Crossrefs

Columns give A002215, A121133-A121136.
Showing 1-3 of 3 results.

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

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