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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198629 Alternating sums of powers of 1,2,...,6, divided by 3. 2
 0, 1, 7, 45, 287, 1821, 11487, 72045, 449407, 2789181, 17230367, 105996045, 649630527, 3968504541, 24174772447, 146908944045, 890924667647, 5393590283901, 32604530573727, 196853323284045, 1187295678104767, 7154833690143261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For the e.g.f.s and o.g.f.s of such alternating power sums see A196847 (even case) and A196848 (odd case). LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720). FORMULA a(n)=sum(((-1)^j)*j^n,j=1..6)/3, n>=0. E.g.f.: sum(((-1)^j)*exp(j*x),j=1..6)/3 = exp(x)*(exp(6*x)-1)/(3*(exp(x)+1)). O.g.f.: sum(((-1)^j)/(1-j*x),j=1..6)/3 = x*(1-14*x+73*x^2-168*x^3+148*x^4)/ product(1-j*x,j=1..6). See A196847 for a formula for the coefficients of the numerator polynomial. MAPLE A198629 := proc(n) (-3^n+4^n-1+2^n-5^n+6^n)/3 ; end proc: seq(A198629(n), n=0..20) ; # R. J. Mathar, May 11 2022 MATHEMATICA Table[Total[Times@@@Partition[Riffle[Range[6]^n, {-1, 1}, {2, -1, 2}], 2]]/3, {n, 0, 30}] (* Harvey P. Dale, Jul 17 2016 *) CROSSREFS Cf. A000225, A083323, 2*A053154, A198628. Sequence in context: A323140 A236194 A230760 * A190973 A099842 A287811 Adjacent sequences: A198626 A198627 A198628 * A198630 A198631 A198632 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Oct 28 2011 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 May 30 02:25 EDT 2023. Contains 363044 sequences. (Running on oeis4.)