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A172447 a(n) = (-1 + 5*2^(2*n + 1) - 3*n)/9. 2
1, 4, 17, 70, 283, 1136, 4549, 18202, 72815, 291268, 1165081, 4660334, 18641347, 74565400, 298261613, 1193046466, 4772185879, 19088743532, 76354974145, 305419896598, 1221679586411, 4886718345664, 19546873382677, 78187493530730, 312749974122943, 1250999896491796 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) mod 10 gives the 10-periodic sequence 1, 4, 7, 0, 3, 6, 9, 2, 5, 8 (and repeat, A131579 shifted, A144468 reversed) which contains all ten digits, that has a "palindromic" symmetry: 1 + 8 = 4 + 5 = 7 + 2 = 0 + 9 = 3 + 6 = 9.
The inverse binomial transform gives 1, 3, 10, 30, 90, ... (A062107 shifted). - R. J. Mathar, Feb 11 2010
LINKS
FORMULA
a(n) = 6*a(n - 1) - 9*a(n - 2) + 4*a(n - 3).
a(n + 1) - 4*a(n) = n.
a(n) = A172416(2n + 1).
G.f.: (1 - 2*x + 2*x^2)/((1 - 4*x) * (x - 1)^2). - R. J. Mathar, Feb 11 2010
E.g.f.: (10*exp(4*x) - (1 + 3*x)*exp(x))/9. - G. C. Greubel, Nov 02 2018
MATHEMATICA
LinearRecurrence[{6, -9, 4}, {1, 4, 17}, 30] (* Harvey P. Dale, Mar 25 2016 *)
((-1 + 5 2^(2# + 1) - 3#)/9 &) /@ Range[0, 29] (* Alonso del Arte, Apr 25 2020 *)
PROG
(Magma) [(-1+5*2^(2*n+1)-3*n)/9: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011
(PARI) a(n)=(10*4^n-3*n)\9 \\ Charles R Greathouse IV, Jul 21 2015
(Scala) val powerOf2: LazyList[BigInt] = LazyList.iterate(1: BigInt)(_ * 2)
(0 to 29).map(n => (-1 + 5 * powerOf2(2 * n + 1) - 3 * n)/9) // Alonso del Arte, Apr 25 2020
CROSSREFS
Cf. A072197 (first differences).
Sequence in context: A005511 A349695 A003127 * A291009 A017955 A017956
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 03 2010
EXTENSIONS
Definition replaced by closed formula by R. J. Mathar, Feb 11 2010
STATUS
approved

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Last modified July 14 19:54 EDT 2024. Contains 374323 sequences. (Running on oeis4.)