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.

A015196 Sum of Gaussian binomial coefficients for q=10.

Original entry on oeis.org

1, 2, 13, 224, 13435, 2266646, 1348019857, 2269339773068, 13484735901526279, 226960944509263279490, 13485189809930561625032701, 2269636415245291711513986785912, 1348523520252401463276762566348539123
Offset: 0

Views

Author

N. J. A. Sloane, Olivier Gérard

Keywords

References

  • J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
  • I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
  • M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Links

Crossrefs

Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122, A015195.
Row sums of triangle A022174.

Programs

  • Mathematica
    Total/@Table[QBinomial[n, m, 10], {n, 0, 20}, {m, 0, n}] (* Vincenzo Librandi, Nov 01 2012 *)
Flatten[{1,RecurrenceTable[{a[n]==2*a[n-1]+(10^(n-1)-1)*a[n-2],a[0]==1,a[1]==2},a,{n,1,15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)

Formula

a(n) = 2*a(n-1)+(10^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013
a(n) ~ c * 10^(n^2/4), where c = EllipticTheta[3,0,1/10]/QPochhammer[1/10,1/10] = 1.348524024616... if n is even and c = EllipticTheta[2,0,1/10]/QPochhammer[1/10,1/10] = 1.2763120346269... if n is odd. - Vaclav Kotesovec, Aug 21 2013

A015197 Sum of Gaussian binomial coefficients for q=11.

Original entry on oeis.org

1, 2, 14, 268, 19156, 3961832, 3092997464, 7024809092848, 60287817008722576, 1505950784990730735392, 142158530752430089391520224, 39060769254069395008311334483648, 40559566021977397260316290099710383936
Offset: 0

Views

Author

N. J. A. Sloane, Olivier Gérard

Keywords

References

  • J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.
  • I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
  • M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Links

Crossrefs

Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122, A015195, A015196.
Row sums of triangle A022175.

Programs

  • Mathematica
    Total/@Table[QBinomial[n, m, 11], {n, 0, 20}, {m, 0, n}] (* Vincenzo Librandi, Nov 02 2012 *)
Flatten[{1,RecurrenceTable[{a[n]==2*a[n-1]+(11^(n-1)-1)*a[n-2],a[0]==1,a[1]==2},a,{n,1,15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)

Formula

a(n) = 2*a(n-1)+(11^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013
a(n) ~ c * 11^(n^2/4), where c = EllipticTheta[3,0,1/11]/QPochhammer[1/11,1/11] = 1.312069129398... if n is even and c = EllipticTheta[2,0,1/11]/QPochhammer[1/11,1/11] = 1.2291712170215... if n is odd. - Vaclav Kotesovec, Aug 21 2013

A348107 a(n) is the number of vector subspaces in (F_9)^n, counted up to coordinate permutation.

Original entry on oeis.org

1, 2, 8, 44, 504, 12128, 810616, 134312136, 65039805696, 77906886854938
Offset: 0

Views

Author

Álvar Ibeas, Sep 30 2021

Keywords

Crossrefs

Row sums of A347975. Cf. A015195.
Showing 1-3 of 3 results.

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

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