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A179903 (1, 3, 5, 7, 9...) convolved with (1, 0, 3, 5, 7, 9,...) 1

%I

%S 1,3,8,21,46,87,148,233,346,491,672,893,1158,1471,1836,2257,2738,3283,

%T 3896,4581,5342,6183,7108,8121,9226,10427,11728,13133,14646,16271,

%U 18012,19873,21858,23971,26216,28597,31118,33783,36596,39561,42682,45963

%N (1, 3, 5, 7, 9...) convolved with (1, 0, 3, 5, 7, 9,...)

%H Vincenzo Librandi, <a href="/A179903/b179903.txt">Table of n, a(n) for n = 0..1000</a>

%H Guo-Niu Han, <a href="http://www-irma.u-strasbg.fr/~guoniu/papers/p77puzzle.pdf">Enumeration of Standard Puzzles</a>

%H Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a> [Cached copy]

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F (1 + 3x + 8x^2 + 21x^3 + ...) = (1 + 3x + 5x^2 + 7x^3 + 9x^4 + ...) * (1 + 3x^2 + 5x^3 + 7x^4 + 9x^5 + ...).

%F a(n) = 2+A005900(n), n>0. G.f.: -(1+x)*(x^3-4*x^2+2*x-1)/(x-1)^4. [From _R. J. Mathar_, Aug 13 2010]

%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - _Vincenzo Librandi_, Jul 04 2012

%e a(5) = 46 = (9, 7, 5, 3, 1) dot (1, 0, 3, 5, 7) = (9 + 0 + 15 + 15 + 7).

%t CoefficientList[Series[-(1+x)*(x^3-4*x^2+2*x-1)/(x-1)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 04 2012 *)

%o (MAGMA) I:=[1, 3, 8, 21, 46]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jul 04 2012

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Jul 31 2010

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)