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 1-9 of 9 results.

A026749 a(n) = T(2n,n-1), T given by A026747.

Original entry on oeis.org

1, 6, 30, 143, 671, 3132, 14601, 68101, 318035, 1487661, 6971222, 32727472, 153926409, 725264305, 3423262180, 16185240446, 76648901377, 363557014067, 1726994886004, 8215502584008, 39135887682617, 186676023857041, 891557875400175
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026750, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(2*n,n-1), n=1..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[2n, n-1], {n,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n, n-1) for n in (1..30)] # G. C. Greubel, Oct 29 2019

A026754 a(n) = Sum{k=0..n} T(n,k), T given by A026747.

Original entry on oeis.org

1, 2, 5, 10, 24, 48, 114, 228, 540, 1080, 2558, 5116, 12133, 24266, 57658, 115316, 274600, 549200, 1310817, 2621634, 6271788, 12543576, 30076629, 60153258, 144550655, 289101310, 696176322, 1392352644, 3359516328
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(add(A026747(n,k), k=0..n), n=0..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[Sum[T[n, k],{k,0,n}], {n,0,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[sum(T(n, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 29 2019

A026748 a(n) = T(2n,n), T given by A026747.

Original entry on oeis.org

1, 3, 11, 44, 184, 790, 3452, 15278, 68290, 307696, 1395696, 6367199, 29193025, 134442102, 621609060, 2884432810, 13428450520, 62703991531, 293606387095, 1378309455352, 6485734373020, 30586630485443, 144544075759391, 684395988590939
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(2*n,n), n=0..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[2n, n], {n,0,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n, n) for n in (0..30)] # G. C. Greubel, Oct 29 2019

A026750 a(n) = T(2n,n-2), T given by A026747.

Original entry on oeis.org

1, 9, 58, 329, 1753, 9020, 45442, 225860, 1112543, 5446607, 26550968, 129042976, 625860205, 3031021096, 14664729519, 70906318405, 342717456708, 1656208470644, 8003645557573, 38681730323747, 186985728069661, 904119336235884
Offset: 2

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026751, A026752, A026753, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(2*n,n-2), n=2..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[2n, n-2], {n,2,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n, n-2) for n in (2..30)] # G. C. Greubel, Oct 29 2019

A026751 a(n) = T(2n-1,n-1), T given by A026747.

Original entry on oeis.org

1, 4, 17, 74, 327, 1461, 6584, 29879, 136391, 625731, 2883357, 13338421, 61920497, 288368511, 1346873365, 6307694990, 29613690966, 139352892908, 657163401162, 3105304341356, 14701236957028, 69722518168060, 331220099616432
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026752, A026753, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(2*n-1,n-1), n=1..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[2n-1, n-1], {n,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n-1, n-1) for n in (1..30)] # G. C. Greubel, Oct 29 2019

A026752 a(n) = T(2n-1,n-2), T given by A026747.

Original entry on oeis.org

1, 7, 39, 201, 1000, 4885, 23621, 113543, 543895, 2600204, 12417829, 59278440, 282969385, 1351124510, 6454283276, 30849969965, 147555219782, 706274470775, 3383203356648, 16219148141581, 77817618006364, 373661751926702
Offset: 2

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026753, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(2*n-1,n-2), n=2..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[2n-1, n-2], {n,2,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(2*n-1, n-2) for n in (2..30)] # G. C. Greubel, Oct 29 2019

A026753 a(n) = T(n, floor(n/2)), T given by A026747.

Original entry on oeis.org

1, 1, 3, 4, 11, 17, 44, 74, 184, 327, 790, 1461, 3452, 6584, 15278, 29879, 68290, 136391, 307696, 625731, 1395696, 2883357, 6367199, 13338421, 29193025, 61920497, 134442102, 288368511, 621609060, 1346873365, 2884432810
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026754, A026755, A026756, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(A026747(n,floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[T[n, Floor[n/2]], {n,0,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[T(n, floor(n/2)) for n in (0..30)] # G. C. Greubel, Oct 29 2019

A026756 a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747.

Original entry on oeis.org

1, 3, 8, 18, 42, 90, 204, 432, 972, 2052, 4610, 9726, 21859, 46125, 103783, 219099, 493699, 1042899, 2353716, 4975350, 11247138, 23790714, 53867343, 114020601, 258571256, 547672566, 1243848888, 2636201532, 5995717860
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026757.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if n<0 then 0;
   elif k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(add(add(A026747(i,j), j=0..n), i=0..n), n=0..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]; Table[Sum[T[i, j], {i,0,n},{j,0,n}], {n,0,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (n<0): return 0
    elif (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[sum(sum(T(i,j) for j in (0..n)) for i in (0..n)) for n in (0..30)] # G. C. Greubel, Oct 29 2019

A026757 a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026747.

Original entry on oeis.org

1, 1, 2, 4, 6, 11, 20, 32, 58, 102, 169, 302, 527, 888, 1573, 2741, 4661, 8215, 14316, 24481, 43023, 74998, 128747, 225867, 393838, 678047, 1188201, 2072239, 3575728, 6261248, 10921278, 18879372, 33040083, 57637061
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A026747, A026748, A026749, A026750, A026751, A026752, A026753, A026754, A026755, A026756.

Programs

  • Maple
    A026747 := proc(n,k) option remember;
   if k=0 or k = n then 1;
   elif type(n,'even') and k <= n/2 then
        procname(n-1,k-1)+procname(n-2,k-1)+procname(n-1,k) ;
   else
       procname(n-1,k-1)+procname(n-1,k) ;
   end if ;
end proc:
seq(add(A026747(n-k,k), k=0..floor(n/2)), n=0..30); # G. C. Greubel, Oct 29 2019
  • Mathematica
    T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[EvenQ[n] && k<=n/2, T[n-1, k -1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]; Table[Sum[T[n-k, k], {k,0,Floor[n/2]}], {n,0,30}] (* G. C. Greubel, Oct 29 2019 *)
  • Sage
    @CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (mod(n,2)==0 and k<=n/2): return T(n-1,k-1) + T(n-2,k-1) + T(n-1,k)
    else: return T(n-1,k-1) + T(n-1,k)
[sum(T(n-k, k) for k in (0..floor(n/2))) for n in (0..30)] # G. C. Greubel, Oct 29 2019
Showing 1-9 of 9 results.

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