The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A217893 50k^2-40k-17 interleaved with 50k^2+10k+13 for k=>0. 1
 -17, 13, -7, 73, 103, 233, 313, 493, 623, 853, 1033, 1313, 1543, 1873, 2153, 2533, 2863, 3293, 3673, 4153, 4583, 5113, 5593, 6173, 6703, 7333, 7913, 8593, 9223, 9953, 10633, 11413, 12143, 12973, 13753, 14633, 15463, 16393, 17273, 18253, 19183, 20213, 21193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The sequence (the fourth in the family) is present as a family of interleaved sequences (five in total) which are separated or factored out to give individual sequences. The first sequence is the parent having the formulas: 50*n^2-100*n+25 and 50*n^2-50*n+25 whose entries are all divisible by 25 and is identical to A178218. The fourth sequence has the formulas 50*n^2-40*n-17 and 50*n^2+10*n+13 and is part of a group where each of the sequences are new, except for the parent (in the factored form). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Eddie Gutierrez New  Interleaved Sequences Part H or Oddwheel.com, Section B1 Line 28 (square_sequencesVIII.html), Part H. Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: (-17+47*x-33*x^2+53*x^3)/((1+x)*(1-x)^3). a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). a(n) = 1+(10*n*(5*n-8)-75*(-1)^n+3)/4. [Bruno Berselli, Oct 15 2012] MATHEMATICA Flatten[Table[{50 n^2 - 40 n - 17, 50 n^2 + 10 n + 13}, {n, 0, 23}]] (* Bruno Berselli, Oct 23 2012 *) CoefficientList[Series[(-17 + 47*x - 33*x^2 + 53*x^3)/((1+x)*(1-x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 15 2012 *) PROG (Magma) &cat[[50*k^2-40*k-17, 50*k^2+10*k+13]: k in [0..23]]; // Bruno Berselli, Oct 23 2012 (PARI) vector(48, n, k=(n-1)\2; if(n%2, 50*k^2-40*k-17, 50*k^2+10*k+13)) \\ Bruno Berselli, Oct 23 2012 CROSSREFS Cf. A178218, A214345, A214393, A214405, A216876. Sequence in context: A279232 A073887 A132955 * A063518 A168250 A089502 Adjacent sequences: A217890 A217891 A217892 * A217894 A217895 A217896 KEYWORD sign,easy AUTHOR Eddie Gutierrez, Oct 14 2012 EXTENSIONS Definition rewritten by Bruno Berselli, Nov 09 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)