A167858 -id:A167858 - cp's OEIS frontend

A166941 Product plus sum of four consecutive nonnegative numbers.

6, 34, 134, 378, 862, 1706, 3054, 5074, 7958, 11922, 17206, 24074, 32814, 43738, 57182, 73506, 93094, 116354, 143718, 175642, 212606, 255114, 303694, 358898, 421302, 491506, 570134, 657834, 755278, 863162, 982206, 1113154, 1256774

Offset: 0

Vladimir Joseph Stephan Orlovsky, Oct 24 2009

a(n) = (n*...*(n+3))+(n+...+(n+3)), n >= 0.
All terms are even.
Binomial transform of 2*A167858.

			a(0) = 0*1*2*3+0+1+2+3 = 0+6 = 6.
a(1) = 1*2*3*4+1+2+3+4 = 24+10 = 34.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A001477 (nonnegative integers), A167858 (3,14,36,36,12,0,0,0,...), A028387 (n+(n+1)^2), A167875, A166942, A166943.

[ &*s + &+s where s is [n..n+3]: n in [0..32] ]; // Klaus Brockhaus, Nov 14 2009

lst={};Do[p=(n+3)*(n+2)*(n+1)*n+(n+3)+(n+2)+(n+1)+n;AppendTo[lst,p],{n,0,5!}];lst

a(n) = n^4 + 6*n^3 + 11*n^2 + 10*n + 6. - Charles R Greathouse IV, Nov 02 2009, [corrected by Klaus Brockhaus, Nov 14 2009]
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24 for n > 3; a(0)=6, a(1)=34, a(2)=134, a(3)=378. - Klaus Brockhaus, Nov 14 2009
G.f.: 2*(3 + 2*x + 12*x^2 - 6*x^3 + x^4)/(1-x)^5. - Klaus Brockhaus, Nov 14 2009

Edited and offset corrected by Klaus Brockhaus, Nov 14 2009

A167876 A000004 preceded by 1, 3, 4, 2.

Original entry on oeis.org

1, 3, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Klaus Brockhaus, Nov 14 2009

Inverse binomial transform of A167875.

Cf. A000004 (zero sequence), A167875 (one third of product plus sum of three consecutive nonnegative integers), A166926 (1, 2, 4, 0, 0, 0, 0, ...), A130706 (1, 2, 0, 0, 0, 0, ...), A130779 (1, 1, 2, 0, 0, 0, 0, ...), A167858 (3, 14, 36, 36, 12, 0, 0, 0, ...).

PARI
```
{concat([1, 3, 4, 2], vector(99))}
```

a(0) = 1, a(1) = 3, a(2) = 4, a(3) = 2, a(n) = 0 for n > 3.

G.f.: (1+x)*(1+2*x+2*x^2).

A167891 A000004 preceded by 1, 4, 2.

Original entry on oeis.org

1, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Klaus Brockhaus, Nov 14 2009

Inverse binomial transform of A028387.

Cf. A000004 (zero sequence), A028387 (n+(n+1)^2), A166926 (1, 2, 4, 0, 0, 0, 0, ...), A130706 (1, 2, 0, 0, 0, 0, ...), A130779 (1, 1, 2, 0, 0, 0, 0, ...), A167858 (3, 14, 36, 36, 12, 0, 0, 0, ...), A167876 (1, 3, 4, 2, 0, 0, 0, ...).

PARI
```
{concat([1, 4, 2], vector(100))}
```

a(0) = 1, a(1) = 4, a(2) = 2, a(n) = 0 for n > 2.

G.f.: 1+4*x+2*x^2.

cp's OEIS Frontend

A166941 Product plus sum of four consecutive nonnegative numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A167876 A000004 preceded by 1, 3, 4, 2.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula

A167891 A000004 preceded by 1, 4, 2.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Formula