

A217893


50k^240k17 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
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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^2100*n+25 and 50*n^250*n+25 whose entries are all divisible by 25 and is identical to A178218. The fourth sequence has the formulas 50*n^240*n17 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*x33*x^2+53*x^3)/((1+x)*(1x)^3).
a(n) = 2*a(n1)2*a(n3)+a(n4).
a(n) = 1+(10*n*(5*n8)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)*(1x)^3), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 15 2012 *)


PROG

(Magma) &cat[[50*k^240*k17, 50*k^2+10*k+13]: k in [0..23]]; // Bruno Berselli, Oct 23 2012
(PARI) vector(48, n, k=(n1)\2; if(n%2, 50*k^240*k17, 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



