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.

User: Brandon Crofts

Brandon Crofts's wiki page.

Brandon Crofts has authored 3 sequences.

A334526 Number of triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 11xy = 0.

Original entry on oeis.org

1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 113, 117, 121, 125, 129, 133, 137, 141, 145, 149, 153, 173, 177, 181, 185, 189, 193, 197, 201, 205, 209, 213, 249, 253, 257, 261, 265, 269, 273, 277, 281, 285, 289, 309, 313, 317
Offset: 0

Author

Brandon Crofts, Jul 10 2020

Keywords

Crossrefs

Cf. A211423.

A334525 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 7xy = 0.

Original entry on oeis.org

1, 5, 9, 13, 17, 21, 25, 37, 41, 45, 49, 53, 57, 61, 81, 85, 89, 93, 97, 101, 105, 125, 129, 133, 137, 141, 145, 149, 185, 189, 193, 197, 201, 205, 209, 229, 233, 237, 241, 245, 249, 253, 297, 301, 305, 309, 313, 317, 321, 333, 337, 341, 345, 349, 353, 357, 393, 397
Offset: 0

Author

Brandon Crofts, Jun 15 2020

Keywords

Comments

If n is squarefree and not divisible by 7, a(n) = a(n-1)+4. - Robert Israel, Jul 01 2020

Crossrefs

Cf. A211423.

Programs

  • Maple
    df:= proc(n) local t, s, m0, m;
       if n mod 7 = 0 then
         m:= n/7;
         t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(7*m^2)))
       else t:= 0
       fi;
       m0:= mul(`if`(s[1]=7, s[1]^ceil((s[2]-1)/2),
           s[1]^ceil(s[2]/2)), s=ifactors(n)[2]);
       t + 4 + 8*floor(n/m0/7);
    end proc:
    df(0):= 1:
    ListTools:-PartialSums(map(df, [$0..100])); # Robert Israel, Jul 01 2020

A334524 Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2 + 5xy = 0.

Original entry on oeis.org

1, 5, 9, 13, 17, 29, 33, 37, 41, 45, 65, 69, 73, 77, 81, 101, 105, 109, 113, 117, 153, 157, 161, 165, 169, 181, 185, 189, 193, 197, 233, 237, 241, 245, 249, 261, 273, 277, 281, 285, 321, 325, 329, 333, 337, 373, 377, 381, 385, 397, 417, 421, 425, 429, 433, 445
Offset: 0

Author

Brandon Crofts, Jun 15 2020

Keywords

Comments

If n is squarefree and not divisible by 5, a(n) = a(n-1)+4. - Robert Israel, Jun 29 2020

Crossrefs

Cf. A211423.

Programs

  • Maple
    df:= proc(n) local t,s,m0,m;
       if n mod 5 = 0 then
         m:= n/5;
         t:= 4*nops(select(s -> s < n and s > m, numtheory:-divisors(5*m^2)))
       else t:= 0
       fi;
       m0:= mul(`if`(s[1]=5, s[1]^ceil((s[2]-1)/2),
           s[1]^ceil(s[2]/2)),s=ifactors(n)[2]);
       t + 4 + 8*floor(n/m0/5);
    end proc:
    df(0):= 1:
    ListTools:-PartialSums(map(df,[$0..100])); # Robert Israel, Jun 29 2020