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 A164123 Partial sums of A162436. 4

%I

%S 1,4,7,16,25,52,79,160,241,484,727,1456,2185,4372,6559,13120,19681,

%T 39364,59047,118096,177145,354292,531439,1062880,1594321,3188644,

%U 4782967,9565936,14348905,28697812,43046719,86093440,129140161

%N Partial sums of A162436.

%C Interleaving of A058481 and A100774 without initial term 0.

%C Apparently a(n) = A062318(n+2)-1 and a(n) = A112346(n+1)-1.

%C The terms beginning with a(2) are the row numbers in Pascalâ€™s Triangle where every 3rd element in those rows is divisible by 3 and none of the other elements in those rows are divisible by 3. - _Thomas M. Green_, Apr 03 2013

%D Thomas M. Green, Prime Patterns in Pascal's Triangle, paper in review process, 2013.

%H Vincenzo Librandi, <a href="/A164123/b164123.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,3,-3).

%F a(n) = A038754(n+1)-2. a(n) = A038754(n+2)-2.

%F a(n) = 3*a(n-2)+4 for n > 2; a(1) = 1, a(2) = 4.

%F a(n) = (5-(-1)^n)*3^(1/4*(2*n-1+(-1)^n))/2-2.

%F G.f.: x*(1+3*x)/((1-x)*(1-3*x^2)).

%e For n = 3, a(3) = 7. The binomial coefficients of the 7th row of Pascal's Triangle are 1 7 21 35 35 21 7 1 and every 3rd element is a multiple of 3. - _Thomas M. Green_, Apr 03 2013

%t Accumulate[Transpose[NestList[{Last[#],3*First[#]}&,{1,3},40]][[1]]] (* _Harvey P. Dale_, Feb 17 2012 *)

%o (MAGMA) T:=[ n le 2 select 2*n-1 else 3*Self(n-2): n in [1..33] ]; [ n eq 1 select T[1] else Self(n-1)+T[n]: n in [1..#T]];

%o (PARI) a(n) = (2+n%2)*3^(n\2)-2 \\ _Charles R Greathouse IV_, Jul 15 2011

%Y Cf. A162436, A058481 (3^n-2), A100774 (2*(3^n - 1)), A062318, A112346, A038754, A038754.

%K nonn,easy

%O 1,2

%A _Klaus Brockhaus_, Aug 10 2009

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