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 1-6 of 6 results.

A154798 Even partition numbers of even numbers.

Original entry on oeis.org

2, 22, 42, 1002, 2436, 3718, 5604, 12310, 37338, 53174, 105558, 204226, 715220, 1300156, 1741630, 2323520, 4087968, 7089500, 12132164, 15796476, 26543660, 34262962, 92669720, 118114304, 150198136, 190569292, 384276336, 483502844
Offset: 1

Views

Author

Omar E. Pol, Jan 26 2009

Keywords

Comments

Even numbers in A058696.

Links

Crossrefs

Cf. A000041, A005843, A058696, A127219, A154795, A154796, A154797.

Programs

  • Maple
    aa:= proc(n, i) if n=0 then 1 elif n<0 or i=0 then 0 else aa(n,i):= aa(n, i-1) +aa(n-i, i) fi end: a:= proc(n) local k; if n>1 then a(n-1) fi; for k from `if`(n=1, 0, b(n-1)+2) by 2 while irem(aa(k, k), 2)=1 do od; b(n):= k; aa(k, k) end: seq(a(n), n=1..40); # Alois P. Heinz, Jul 28 2009
  • Mathematica
    Select[Table[PartitionsP[n], {n, 0, 200, 2}], EvenQ] (* Jean-François Alcover, Aug 28 2015 *)
  • PARI
    select(x->!(x%2), vector(80, n, numbpart(2*n))) \\ Michel Marcus, Aug 28 2015

Extensions

More terms from Alois P. Heinz, Jul 28 2009

A154795 Odd partition numbers of odd numbers.

Original entry on oeis.org

1, 3, 7, 15, 101, 297, 1255, 4565, 10143, 14883, 21637, 31185, 44583, 63261, 173525, 239943, 329931, 1121505, 1505499, 2679689, 3554345, 4697205, 6185689, 10619863, 18004327, 23338469, 30167357, 38887673, 49995925, 64112359, 82010177
Offset: 1

Views

Author

Omar E. Pol, Jan 26 2009

Keywords

Comments

Odd numbers in A058695.

Examples

			7 is in the sequence because the odd number 5 has partition number 7 (5,41,32,311,2221,22111,1111111). - _Emeric Deutsch_, Aug 02 2009

Links

Crossrefs

Cf. A000041, A005408, A058695, A154796, A154797, A154798.

Programs

  • Maple
    aa:= proc(n, i) if n=0 then 1 elif n<0 or i=0 then 0 else aa(n,i):= aa(n, i-1) +aa(n-i, i) fi end: a:= proc(n) local k; if n>1 then a(n-1) fi; for k from `if`(n=1, 1, b(n-1)+2) by 2 while irem(aa(k, k), 2)=0 do od; b(n):= k; aa(k, k) end: seq(a(n), n=1..40); # Alois P. Heinz, Jul 28 2009
with(combinat): a := proc (n) if `mod`(numbpart(2*n-1), 2) = 1 then numbpart(2*n-1) else end if end proc: seq(a(n), n = 1 .. 50); # Emeric Deutsch, Aug 02 2009
  • Mathematica
    Reap[Do[If[OddQ[p = PartitionsP[n]], Sow[p]], {n, 1, 99, 2}]][[2, 1]] (* Jean-François Alcover, Aug 31 2015 *)

Extensions

More terms from Alois P. Heinz, Jul 28 2009

A154796 Even partition numbers of odd numbers.

Original entry on oeis.org

30, 56, 176, 490, 792, 1958, 3010, 6842, 89134, 124754, 451276, 614154, 831820, 2012558, 8118264, 13848650, 133230930, 214481126, 271248950, 541946240, 851376628, 1327710076, 3163127352, 4835271870, 5964539504, 7346629512
Offset: 1

Views

Author

Omar E. Pol, Jan 26 2009

Keywords

Comments

Even numbers in A058695.

Examples

			The even number 30 is in the sequence as the partition number of the odd number 9. - _Emeric Deutsch_, Aug 02 2009

Links

Crossrefs

Cf. A000041, A005408, A058695, A154795, A154797, A154798.

Programs

  • Maple
    aa:= proc(n, i) if n=0 then 1 elif n<0 or i=0 then 0 else aa(n,i):= aa(n, i-1) +aa(n-i, i) fi end: a:= proc(n) local k; if n>1 then a(n-1) fi; for k from `if`(n=1, 1, b(n-1)+2) by 2 while irem(aa(k, k), 2)=1 do od; b(n):= k; aa(k, k) end: seq(a(n), n=1..40); # Alois P. Heinz, Jul 28 2009
with(combinat): a := proc (n) if `mod`(numbpart(2*n-1), 2) = 0 then numbpart(2*n-1) else end if end proc: seq(a(n), n = 1 .. 70); # Emeric Deutsch, Aug 02 2009
  • Mathematica
    Reap[Do[If[EvenQ[p = PartitionsP[n]], Sow[p]], {n, 1, 199, 2}]][[2, 1]] (* Jean-François Alcover, Nov 11 2015 *)
Select[PartitionsP[Range[1,201,2]],EvenQ] (* Harvey P. Dale, Apr 03 2019 *)
  • PARI
    lista(nn) = for (n=1, nn, if (((p = numbpart(2*n+1)) % 2) == 0, print1(p, ", "))); \\ Michel Marcus, Dec 19 2016

Extensions

More terms from Alois P. Heinz, Jul 28 2009

A163097 Even numbers with an odd number of partitions.

Original entry on oeis.org

0, 4, 6, 12, 14, 16, 18, 20, 24, 32, 36, 38, 44, 48, 52, 54, 56, 60, 68, 72, 76, 82, 88, 90, 92, 102, 104, 114, 118, 132, 134, 138, 140, 144, 146, 148, 150, 152, 156, 162, 164, 166, 168, 172, 178, 182, 186, 188, 190, 192, 194, 196, 202, 204, 208, 210, 212, 214, 216
Offset: 1

Views

Author

Omar E. Pol, Aug 09 2009

Keywords

Crossrefs

Cf. A000041, A005843, A052002, A127219, A154797, A163096, A163099.

Programs

  • Mathematica
    Select[2*Range[0,150],OddQ[PartitionsP[#]]&] (* Harvey P. Dale, Nov 13 2013 *)

Extensions

More terms from Sean A. Irvine, Oct 26 2009

A209659 Partition numbers p(n) having opposite parity of n.

Original entry on oeis.org

1, 5, 11, 30, 56, 77, 135, 176, 231, 385, 490, 627, 792, 1575, 1958, 3010, 6842, 8349, 17977, 26015, 75175, 89134, 124754, 147273, 281589, 386155, 451276, 526823, 614154, 831820, 966467, 2012558, 3087735, 5392783, 8118264, 9289091, 13848650
Offset: 1

Views

Author

Omar E. Pol, Mar 22 2012

Keywords

Comments

Union of A154797 and A154796. The union of this sequence and A209658 gives A000041.

Links

Crossrefs

Cf. A000041, A052001, A052003, A067567, A127219, A154795-A154798, A163096, A163097, A194798, A209658, A209920.

A163099 a(n) = A163097(n)/2.

Original entry on oeis.org

0, 2, 3, 6, 7, 8, 9, 10, 12, 16, 18, 19, 22, 24, 26, 27, 28, 30, 34, 36, 38, 41, 44, 45, 46, 51, 52, 57, 59, 66, 67, 69, 70, 72, 73, 74, 75, 76, 78, 81, 82, 83, 84, 86, 89, 91, 93, 94, 95, 96, 97, 98, 101, 102, 104, 105, 106, 107, 108
Offset: 1

Views

Author

Omar E. Pol, Aug 09 2009

Keywords

Crossrefs

Cf. A000041, A154797, A163097.

Extensions

More terms from Max Alekseyev, Aug 23 2013
Showing 1-6 of 6 results.

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