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 1-7 of 7 results.

A163286 a(n) = A154796(n)/2.

Original entry on oeis.org

15, 28, 88, 245, 396, 979, 1505, 3421, 44567, 62377, 225638, 307077, 415910, 1006279, 4059132, 6924325, 66615465, 107240563, 135624475, 270973120, 425688314, 663855038, 1581563676, 2417635935, 2982269752, 3673314756, 4517918038, 5548822508, 8335344604, 15194335989
Offset: 1

Views

Author

Omar E. Pol, Aug 09 2009

Keywords

Links

Crossrefs

Cf. A000041, A154796, A163096.

Programs

  • Mathematica
    (1/2)*Reap[Do[If[EvenQ[p = PartitionsP[n]], Sow[p]], {n, 1, 500, 2}]][[2, 1]] (* G. C. Greubel, Dec 17 2016 *)
  • PARI
    lista(nn) = for (n=1, nn, if (((p = numbpart(2*n+1)) % 2) == 0, print1(p/2, ", "))); \\ Michel Marcus, Dec 17 2016

Extensions

More terms from R. J. Mathar, Sep 27 2009

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

A163096 Odd numbers with an even number of partitions.

Original entry on oeis.org

9, 11, 15, 19, 21, 25, 27, 31, 45, 47, 55, 57, 59, 65, 75, 79, 97, 101, 103, 109, 113, 117, 125, 129, 131, 133, 135, 137, 141, 147, 149, 151, 153, 163, 167, 171, 175, 179, 187, 191, 197, 205, 207, 213, 217, 227, 231, 241, 243, 245, 247, 253, 255, 265, 267, 271
Offset: 1

Views

Author

Omar E. Pol, Aug 09 2009

Keywords

Links

Crossrefs

Cf. A000041, A001560, A005408, A154796, A163097.

Programs

  • Mathematica
    Select[Range[1,500,2],EvenQ[PartitionsP[#]]&] (* Vincenzo Librandi, Mar 19 2012 *)

Extensions

More terms from Sean A. Irvine, Oct 26 2009

A154797 Odd partition numbers of even numbers.

Original entry on oeis.org

1, 5, 11, 77, 135, 231, 385, 627, 1575, 8349, 17977, 26015, 75175, 147273, 281589, 386155, 526823, 966467, 3087735, 5392783, 9289091, 20506255, 44108109, 56634173, 72533807, 241265379, 304801365, 952050665, 1482074143, 6620830889
Offset: 1

Views

Author

Omar E. Pol, Jan 26 2009

Keywords

Comments

Odd numbers in A058696.

Examples

			The odd number 5 is in the sequence as the partition number of the even number 4: (4, 3+1, 2+2, 2+1+1, 1+1+1+1). - _Emeric Deutsch_, Aug 02 2009

Links

Crossrefs

Cf. A000041, A005843, A058696, A154795, A154796, 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, 0, 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), 2) = 1 then numbpart(2*n) else end if end proc: seq(a(n), n = 0 .. 70); # Emeric Deutsch, Aug 02 2009
  • Mathematica
    Select[PartitionsP[2*Range[0,100]],OddQ] (* Harvey P. Dale, Nov 30 2014 *)

Extensions

More terms from Alois P. Heinz, Jul 28 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.

A193830 Even partition numbers of prime numbers.

Original entry on oeis.org

2, 56, 490, 6842, 124754, 831820, 13848650, 133230930, 214481126, 271248950, 541946240, 851376628, 5964539504, 11097645016, 37027355200, 45060624582, 142798995930, 207890420102, 625846753120, 1820701100652, 3068829878530, 37561133582570, 114540884553038
Offset: 1

Views

Author

Omar E. Pol, Aug 06 2011

Keywords

Examples

			The even number 56 is in the sequence as the partition number of the prime number 11.

Crossrefs

Even numbers in A058698.
Cf. A000040, A000041, A052001, A154796, A154798, A163997, A193831.

Programs

  • Mathematica
    Select[PartitionsP[Prime[Range[200]]],EvenQ] (* Harvey P. Dale, Jun 20 2015 *)
Showing 1-7 of 7 results.

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