The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A261800 Number of 8-compositions of n: matrices with 8 rows of nonnegative integers with positive column sums and total element sum n. 2
 1, 8, 100, 1208, 14554, 175352, 2112772, 25456328, 306717703, 3695574048, 44527157584, 536497912672, 6464145163032, 77885061063584, 938419943222768, 11306815168562400, 136233325153964242, 1641445323534504928, 19777413104380161776, 238293693669343744032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the number of compositions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..925 Index entries for linear recurrences with constant coefficients, signature (16,-56,112,-140,112,-56,16,-2). FORMULA G.f.: (1-x)^8/(2*(1-x)^8-1). a(n) = A261780(n,8). a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+8*k,n). - Seiichi Manyama, Aug 06 2024 MAPLE a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*binomial(j+7, 7), j=1..n)) end: seq(a(n), n=0..20); MATHEMATICA CoefficientList[Series[(1-x)^8/(2(1-x)^8-1), {x, 0, 30}], x] (* or *) LinearRecurrence[{16, -56, 112, -140, 112, -56, 16, -2}, {1, 8, 100, 1208, 14554, 175352, 2112772, 25456328, 306717703}, 30] (* Harvey P. Dale, Jul 15 2023 *) CROSSREFS Column k=8 of A261780. Sequence in context: A229282 A179485 A144072 * A208705 A246237 A234513 Adjacent sequences: A261797 A261798 A261799 * A261801 A261802 A261803 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Sep 01 2015 STATUS approved

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

Last modified September 18 08:17 EDT 2024. Contains 375997 sequences. (Running on oeis4.)