login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123203 A007318 * [1, 1, 4, 4, 4,...]. 8
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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..30.

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: (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 *)

CROSSREFS

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

Sequence in context: A090145 A244307 A270109 * 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

The two given formulas corrected by Colin Barker, Jul 28 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 15 03:16 EDT 2021. Contains 343909 sequences. (Running on oeis4.)