login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A158943 INVERT transform of A027656: (1, 0, 2, 0, 3, 0, 4, 0, 5,...) 4
1, 1, 3, 5, 10, 19, 36, 69, 131, 250, 476, 907, 1728, 3292, 6272, 11949, 22765, 43371, 82629, 157422, 299915, 571388, 1088589, 2073943, 3951206, 7527704, 14341527, 27322992, 52054840, 99173120, 188941273, 359964521, 685792227, 1306548149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equals row sums of triangle A158945.

Number of compositions of n into odd parts where there is 1 sort of part 1, 2 sorts of part 3, 3 sorts of part 5, ... , k sorts of part 2*k-1. - Joerg Arndt, Aug 04 2014

LINKS

Table of n, a(n) for n=1..34.

FORMULA

INVERT transform of (1, 0, 2, 0, 3, 0, 4,...); i.e. the natural numbers interleaved with zeros.

a(n)=a(n-1)+2a(n-2)-a(n-4). G.f.: x/(1-x-2*x^2+x^4). [From R. J. Mathar, Apr 02 2009]

EXAMPLE

The INVERT transform of (1, N,...) begins (1, (N+1),...) so that we have (1, 1,...) placed in ascending magnitude in the bottom row. In the top row we place an equal number of descending terms: (...0, 3, 0, 2, 0, 1). Take the dot product of terms in top and bottom rows, adding the result to the next term A027656: (1, 0, 2, 0, 3,...). a(6) = 19 given: 3, 0, 2, 0, 1 1, 1, 3, 5, 10 Dot product of top row terms * bottom row terms = (1, 0, 2, 0, 3) dot (1, 1, 3, 5, 10)

= (3 + 0 + 6 + 0 + 10) = 19, which is added to the next term in (1, 0, 2, 0, 3,...); i.e. (an 0) = 19.

MAPLE

A027656 := proc(n) if type(n, odd) then 0; else n/2+1 ; fi; end: L := [seq(A027656(n), n=0..100)] ; read("transforms"); INVERT(L) ; # R. J. Mathar, Apr 02 2009

CROSSREFS

Cf. A158944, A158945, A027656

Sequence in context: A270715 A291735 A261050 * A133999 A238431 A014610

Adjacent sequences:  A158940 A158941 A158942 * A158944 A158945 A158946

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Mar 31 2009

EXTENSIONS

Extended by R. J. Mathar, Apr 02 2009

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 21 22:24 EDT 2019. Contains 323467 sequences. (Running on oeis4.)