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 1-5 of 5 results.

A227364 a(n) = 1 + 2*3 + 4*5*6 + 7*8*9*10 + ... + ...*n (see Example lines).

Original entry on oeis.org

0, 1, 3, 7, 11, 27, 127, 134, 183, 631, 5167, 5178, 5299, 6883, 29191, 365527, 365543, 365799, 370423, 458551, 2226007, 39435607, 39435629, 39436113, 39447751, 39739207, 47329207, 252562807, 6006997207, 6006997236, 6006998077, 6007024177, 6007860247, 6035477527, 6975328087
Offset: 0

Views

Author

Alex Ratushnyak, Jul 07 2013

Keywords

Examples

			a(5) = 1 + 2*3 + 4*5 = 27;
a(6) = 1 + 2*3 + 4*5*6 = 127;
a(7) = 1 + 2*3 + 4*5*6 + 7 = 134.

Links

Crossrefs

Cf. A227363, A227365, A227366, A227367, A228958.

Programs

  • Python
    for n in range(55):
  sum = 0
  i = k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= i
      i += 1
      if i>n: break
    sum += product
    k += 1
  print(str(sum), end=',')

A227365 a(n) = 0 + 1*2 + 3*4*5 + 6*7*8*9 + ... + ...*n.

Original entry on oeis.org

0, 1, 2, 5, 14, 62, 68, 104, 398, 3086, 3096, 3196, 4406, 20246, 243326, 243341, 243566, 247406, 316766, 1638686, 28150526, 28150547, 28150988, 28161152, 28405550, 34526126, 193916126, 4503821726, 4503821754, 4503822538, 4503846086, 4504576886, 4527986846, 5301270686
Offset: 0

Views

Author

Alex Ratushnyak, Jul 07 2013

Keywords

Examples

			a(4) = 0 + 1*2 + 3*4 = 14.
a(5) = 0 + 1*2 + 3*4*5 = 62.
a(6) = 0 + 1*2 + 3*4*5 + 6 = 68.

Links

Crossrefs

Cf. A227363, A227364, A227366, A227367.

Programs

  • Python
    for n in range(55):
  sum = i = 0
  k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= i
      i += 1
      if i>n: break
    sum += product
    k += 1
  print(str(sum), end=',')

A227367 a(0)=1, a(n+1) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) + a(6)*a(7)*a(8)*a(9) + ... + ...*a(n).

Original entry on oeis.org

1, 1, 2, 3, 6, 21, 381, 762, 290703, 84397476747, 7122934049104967061783, 14245868098209934123566, 101472378935797762635619628499635817245339961, 10296643686890133479148472187437767614663729545766251948487237380959682684821520304732841
Offset: 0

Views

Author

Alex Ratushnyak, Jul 08 2013

Keywords

Examples

			a(1) = a(0) = 1
a(2) = a(0) + a(1) = 2
a(3) = a(0) + a(1)*a(2) = 3
a(4) = a(0) + a(1)*a(2) + a(3) = 1 + 2 + 3 = 6
a(5) = a(0) + a(1)*a(2) + a(3)*a(4) = 1 + 2 + 18 = 21
a(6) = a(0) + a(1)*a(2) + a(3)*a(4)*a(5) = 1 + 2 + 18*21 = 381

Crossrefs

Cf. A227363, A227364, A227365, A227366.

Programs

  • Python
    a = [1]*99
for n in range(20):
  sum = i = 0
  k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= a[i]
      i += 1
      if i>n: break
    sum += product
    k += 1
  a[n+1] = sum
  print(str(a[n]),end=',')

A227366 a(0)=1, a(n+1) = a(n) + a(n-1)*a(n-2) + a(n-3)*a(n-4)*a(n-5) + a(n-6)*a(n-7)*a(n-8)*a(n-9) + ... + ...*a(0).

Original entry on oeis.org

1, 1, 2, 3, 6, 13, 33, 118, 584, 4714, 76206, 2879841, 364389490, 220150411628, 1049813737275512, 80222580570107370160, 231117086585854944888597249, 84218767584329653007205530276477742, 18540809099930664963747242025045529905738135516
Offset: 0

Views

Author

Alex Ratushnyak, Jul 08 2013

Keywords

Examples

			a(1) = a(0) = 1
a(2) = a(1) + a(0) = 2
a(3) = a(2) + a(1)*a(0) = 3
a(4) = a(3) + a(2)*a(1) + a(0) = 3 + 2 + 1 = 6
a(5) = a(4) + a(3)*a(2) + a(1)*a(0) = 6 + 3*2 + 1 = 13

Crossrefs

Cf. A227363, A227364, A227365, A227367.

Programs

  • Python
    a = [1]*99
for n in range(20):
  sum = i = 0
  k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= a[n-i]
      i += 1
      if i>n: break
    sum += product
    k += 1
  a[n+1] = sum
  print(str(a[n]),end=',')

A239519 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*1.

Original entry on oeis.org

0, 1, 3, 5, 11, 19, 32, 62, 112, 191, 316, 558, 988, 1711, 2864, 4661, 7703, 12883, 21626, 35989, 58826, 94217, 150017, 239047, 382676, 614425, 984452, 1565021, 2458810, 3826746, 5918938, 9136603, 14115710, 21842345, 33804340, 52186061, 80128082, 122221802
Offset: 0

Views

Author

Alex Ratushnyak, Mar 20 2014

Keywords

Comments

In other words, write n,n-1,n-2,...,n-k,...,1 and place '+' before the terms n-k, where k is triangular, place '*' elsewhere, then a(n) = result. - Ralf Stephan, Mar 29 2014

Examples

			a(2) = 2 + 1 = 3.
a(3) = 3 + 2*1 = 5.
a(9) = 9 + 8*7 + 6*5*4 + 3*2*1 = 191.
a(10) = 10 + 9*8 + 7*6*5 + 4*3*2*1 = 316.

Crossrefs

Cf. A227363-A227367.

Programs

  • Python
    for n in range(55):
  sum_ = i = 0
  k = 1
  while i=n:  break
    sum_ += product
    k += 1
  print(sum_, end=', ')
Showing 1-5 of 5 results.

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