A123203 A007318 * [1, 1, 4, 4, 4, ...].

1, 2, 7, 20, 49, 110, 235, 488, 997, 2018, 4063, 8156, 16345, 32726, 65491, 131024, 262093, 524234, 1048519, 2097092, 4194241, 8388542, 16777147, 33554360, 67108789, 134217650, 268435375, 536870828, 1073741737, 2147483558

Offset

1,2

Comments

An elephant sequence, see A175654. For the corner squares just one A[5] vector, with decimal value 186, leads to this sequence. For the central square this vector leads to the companion sequence A036563. - Johannes W. Meijer, Aug 15 2010

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Tamas Lengyel, On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory, 148 (2015) 73-94.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

Binomial transform of [1, 1, 4, 4, 4, ...]. Row sums of triangle A131061.

From Johannes W. Meijer, Aug 15 2010; corrected by Colin Barker, Jul 28 2012: (Start)

a(n) = 2^(1+n) - 3*n.

a(n) = 3*A000295(n-1) + A000079(n-1).

(End)

G.f.: x*(1 - 2*x + 4*x^2)/((1-x)^2*(1-2*x)). - Colin Barker, Jul 28 2012

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Colin Barker, Jul 29 2012

Example

a(4) = 20, row sums of 4th row of triangle A131062: (1, 9, 9, 1).
a(4) = 20 = (1, 3, 3, 1) dot (1, 1, 4, 4) = (1 + 3 + 12 + 4).

Mathematica

s=1; lst={s}; Do[s+=(s+=n)+n++; AppendTo[lst, s], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
LinearRecurrence[{4, -5, 2}, {1, 2, 7}, 40] (* Harvey P. Dale, Mar 30 2024 *)

Crossrefs

Cf. A109128, A131060, A131061, A131063, A131064, A131065, A131066.

Sequence in context: A368881 A270109 A360421 * A309298 A335927 A261054

Adjacent sequences: A123200 A123201 A123202 * A123204 A123205 A123206

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 13 2007

Extensions

More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008

Status

approved