The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001769 Expansion of 1/((1+x)*(1-x)^7). 12
 1, 6, 22, 62, 148, 314, 610, 1106, 1897, 3108, 4900, 7476, 11088, 16044, 22716, 31548, 43065, 57882, 76714, 100386, 129844, 166166, 210574, 264446, 329329, 406952, 499240, 608328, 736576, 886584, 1061208, 1263576, 1497105, 1765518, 2072862, 2423526, 2822260, 3274194, 3784858 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 17. Index entries for linear recurrences with constant coefficients, signature (6,-14,14,0,-14,14,-6,1). FORMULA From Paul Barry, Jul 01 2003: (Start) a(n) = Sum_{k=0..n} (-1)^(n-k)*C(k+6, 6). a(n) = (4*n^6 +96*n^5 +910*n^4 +4320*n^3 +10696*n^2 +12864*n+5715)/5760+(-1)^n/128. (End) Boas-Buck recurrence: a(n) = (1/n)*Sum_{p=0..n-1} (7 + (-1)^(n-p))*a(p), n >= 1, a(0) = 1. See the Boas-Buck comment in A046521 (here for the unsigned column k = 3 with offset 0). a(n)+a(n+1) = A000579(n+7). - R. J. Mathar, Jan 06 2021 MATHEMATICA CoefficientList[Series[1/((1+x)(1-x)^7), {x, 0, 30}], x] (* or *) LinearRecurrence[ {6, -14, 14, 0, -14, 14, -6, 1}, {1, 6, 22, 62, 148, 314, 610, 1106}, 40] (* Harvey P. Dale, May 24 2015 *) PROG (Magma) [(4*n^6+96*n^5+910*n^4+4320*n^3+10696*n^2+12864*n+5715)/5760+(-1)^n/128: n in [0..40]]; // Vincenzo Librandi, Aug 15 2011 (PARI) a(n)=(4*n^6+96*n^5+910*n^4+4320*n^3+10696*n^2+12864*n)\/5760+1 \\ Charles R Greathouse IV, Apr 17 2012 CROSSREFS Cf. A002620, A002623, A001752, A001753 (first differences), A158454 (signed column k=3), A001779 (partial sums), A169794 (binomial transf.). Sequence in context: A105450 A011888 A081282 * A166020 A307621 A257200 Adjacent sequences: A001766 A001767 A001768 * A001770 A001771 A001772 KEYWORD nonn,easy AUTHOR N. J. A. Sloane 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 18 15:59 EDT 2024. Contains 372664 sequences. (Running on oeis4.)