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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A005961 Number of acyclic disubstituted alkanes with n carbon atoms and identical substituents.

Original entry on oeis.org

1, 2, 5, 13, 37, 108, 325, 993, 3070, 9564, 29979, 94392, 298311, 945592, 3005021, 9570559, 30539044, 97611676, 312462096, 1001554565, 3214232129, 10326580526, 33210135104, 106901289420, 344398593149, 1110395171502, 3582666470285, 11567123373968
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Acyclic alkanes of the form C_nH_mX2. - Sean A. Irvine, Nov 12 2016

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005960.

Formula

G.f.: -1 + (1/(1-x*B(x)^2) + 1/(1-x*B(x^2)))/2 where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

Extensions

More terms and title improved by Sean A. Irvine, Nov 12 2016

A193418 Expansion of x*(x^2+x-1)/(3*x^6-4*x^5+x^4-3*x^2+4*x-1).

Original entry on oeis.org

1, 3, 8, 23, 69, 206, 616, 1846, 5537, 16609, 49824, 149469, 448405, 1345212, 4035632, 12106892, 36320673, 108962015, 326886040, 980658115, 2941974341, 8825923018, 26477769048, 79433307138, 238299921409, 714899764221, 2144699292656
Offset: 1

Views

Author

Yalcin Aktar, Jul 26 2011

Keywords

Comments

Conjecture: log(A005960-a(n)) ~ (log(2)*(2*n-11)).

Crossrefs

Cf. A005960.

Formula

a(n) = b(n+1,3)-b(n+1,4) with b(n,c) = sum(floor(3^m/2^c), m=1..n).
G.f.: x*(x^2+x-1) / (3*x^6-4*x^5+x^4-3*x^2+4*x-1).
a(n) = (9*3^n+4*n+1-(1+(-1)^n)*(1+4*i^n))/32, where i=sqrt(-1). - Bruno Berselli, Jul 30 2011
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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