A227366 -id:A227366 - cp's OEIS frontend

A227364 a(n) = 1 + 23 + 456 + 78910 + ... + ...*n (see Example lines).

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

Alex Ratushnyak, Jul 07 2013

nonn

			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.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

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

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=',')

A227363 a(n) = n + (n-1)(n-2) + (n-3)(n-4)(n-5) + (n-6)(n-7)(n-8)(n-9) + ... + ...*(n-n).

Original entry on oeis.org

0, 1, 2, 5, 10, 17, 32, 61, 110, 185, 316, 557, 986, 1705, 2840, 4661, 7702, 12881, 21620, 35965, 58706, 94217, 150016, 239045, 382670, 614401, 984332, 1564301, 2458810, 3826745, 5918936, 9136597, 14115686, 21842225, 33803620, 52181021, 80128082, 122221801, 185211440

Offset: 0

Alex Ratushnyak, Jul 07 2013

nonn

From a question by Jonathan Vos Post dated Jul 09 2013, the indices of a(n) which are prime begin: 2, 3, 5, 7, 11, 41, 111, 205, 211, 215, 341, 345, 395, 581, 585, 1221, ..., . - Robert G. Wilson v, Jul 10 2013

			a(2) = 2 + 1*0 = 2.
a(3) = 3 + 2*1 = 5.
a(9) = 9 + 8*7 + 6*5*4 + 3*2*1*0 = 9 + 56 + 120 = 185.
a(11) = 11 + 10*9 + 8*7*6 + 5*4*3*2 = 557.
a(18) = 18 + 17*16 + 15*14*13 + 12*11*10*9 + 8*7*6*5*4 = 21620.

Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Cf. A227364, A227365, A227366, A227367.

f[n_] := Sum[ Product[ n - k (k - 1)/2 - i + 1, {i, k}], {k, Sqrt[ 2n]}]; Array[f, 39, 0] (* Robert G. Wilson v, Jul 10 2013 *)

a(n)=sum(k=1,sqrtint(2*n)+1,prod(i=1,k,max(n-k*(k-1)/2-i+1,0))) \\ Charles R Greathouse IV, Jul 09 2013

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

A227365 a(n) = 0 + 12 + 345 + 6789 + ... + ...*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

Alex Ratushnyak, Jul 07 2013

nonn

			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.

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A227363, A227364, A227366, A227367.

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

Alex Ratushnyak, Jul 08 2013

nonn

			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

Cf. A227363, A227364, A227365, A227366.

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=',')

cp's OEIS Frontend

A227364 a(n) = 1 + 23 + 456 + 78910 + ... + ...*n (see Example lines).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A227363 a(n) = n + (n-1)(n-2) + (n-3)(n-4)(n-5) + (n-6)(n-7)(n-8)(n-9) + ... + ...*(n-n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A227365 a(n) = 0 + 12 + 345 + 6789 + ... + ...*n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

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).

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A227363 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*(n-n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

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).

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

A227364 a(n) = 1 + 23 + 456 + 78910 + ... + ...*n (see Example lines).

A227363 a(n) = n + (n-1)(n-2) + (n-3)(n-4)(n-5) + (n-6)(n-7)(n-8)(n-9) + ... + ...*(n-n).

A227365 a(n) = 0 + 12 + 345 + 6789 + ... + ...*n.

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).