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.

A379588 Antidiagonal sums of the array A379587.

Original entry on oeis.org

0, 1, 11, 84, 642, 5633, 59021, 736944, 10839316, 185361065, 3637063343, 80939054884, 2023405966486, 56362728831929, 1736960568923505, 58853395571312176, 2180579093801111176, 87921539854223957169, 3841160785119756991059
Offset: 0

Views

Author

Stefano Spezia, Dec 26 2024

Keywords

Crossrefs

Programs

  • Mathematica
    A379587[n_,k_]:=(k^n-1)^2/(k-1); a[n_]:=Sum[A379587[n-k+2,k],{k,2,n+2}]; Array[a,15,0]

Formula

a(n) = Sum_{k=2..n+2} (k^(n-k+2) - 1)^2/(k - 1).

A060869 Number of n X n matrices over GF(4) with rank 1.

Original entry on oeis.org

3, 75, 1323, 21675, 348843, 5589675, 89467563, 1431612075, 22906317483, 366503176875, 5864059218603, 93824981052075, 1501199831050923, 24019197833685675, 384307167486454443, 6148914688373205675, 98382635048331029163, 1574122160910735420075, 25185954575121522535083
Offset: 1

Views

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

Keywords

Examples

			a(2) = 75 because there are 76 (the second element in sequence A060716) singular 2 X 2 matrices over GF(4), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 76 - 1 = 75.
		

Crossrefs

Column k=4 of A379587.
Cf. A060716.

Programs

Formula

a(n) = 1/3 * (4^n - 1)^2.
G.f.: -3*x*(4*x+1) / ((x-1)*(4*x-1)*(16*x-1)). - Colin Barker, Dec 23 2012
E.g.f.: exp(x)*(1 - 2*exp(3*x) + exp(15*x))/3. - Stefano Spezia, Dec 26 2024

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, May 07 2001
More terms from Colin Barker, Dec 23 2012

A060868 Number of n X n matrices over GF(3) with rank 1.

Original entry on oeis.org

2, 32, 338, 3200, 29282, 264992, 2389298, 21516800, 193690562, 1743333152, 15690352658, 141214236800, 1270931319842, 11438391444512, 102945551698418, 926510051379200, 8338590720693122, 75047317261079072, 675425857674234578, 6078832726041680000, 54709494555295826402
Offset: 1

Views

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001

Keywords

Examples

			a(2) = 32 because there are 33 (the second element in sequence A060705) singular 2 X 2 matrices over GF(3), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 33 - 1 = 32.
		

Crossrefs

Column k=3 of A379587.

Programs

Formula

a(n) = 1/2 * (3^n - 1)^2.
G.f.: -2*x*(3*x+1) / ((x-1)*(3*x-1)*(9*x-1)). - Colin Barker, Dec 23 2012
E.g.f.: exp(x)*(1 - 2*exp(2*x) + exp(8*x))/2. - Stefano Spezia, Dec 26 2024

Extensions

More terms from Jason Earls, May 05 2001
Showing 1-3 of 3 results.