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 A107659 a(n) = Sum_{k=0..n} 2^max(k, n-k). 3

%I

%S 1,4,10,24,52,112,232,480,976,1984,4000,8064,16192,32512,65152,130560,

%T 261376,523264,1047040,2095104,4191232,8384512,16771072,33546240,

%U 67096576,134201344,268410880,536838144,1073692672,2147418112

%N a(n) = Sum_{k=0..n} 2^max(k, n-k).

%C Define an infinite array by m(n,k) = 2^n-n+k for n>=k>=0 (in the lower left triangle) and by m(n,k) = 2^k+k-n for k>=n>=0 (in the upper right triangle). The antidiagonal sums of this array are a(n) = sum_{k=0..n} m(n-k,k). - _J. M. Bergot_, Aug 16 2013

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-4).

%F a(2n) = 2^n(2^(n+2)-3), a(2n+1) = 2^n(2^(n+3)-4).

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

%F a(n) = A122746(n) +2*A122746(n-1). - _R. J. Mathar_, Aug 16 2013

%F a(0)=1, a(1)=4, a(2)=10, a(n)=2*a(n-1)+2*a(n-2)-4*a(n-3). - _Harvey P. Dale_, Nov 10 2013

%F a(n) = 2^(n+2) - (2 + mod(n+1, 2)) * 2^floor((n+1)/2). - _Michael Somos_, Jun 24 2018

%F a(n) = - (2^(n+2)) * A052955(-n-3) for all n in Z. - _Michael Somos_, Jun 24 2018

%e G.f. = 1 + 4*x + 10*x^2 + 24*x^3 + 52*x^4 + 112*x^5 + 232*x^6 + 480*x^7 + ... - _Michael Somos_, Jun 24 2018

%t Table[Sum[2^Max[k,n-k],{k,0,n}],{n,0,30}] (* or *) LinearRecurrence[ {2,2,-4},{1,4,10},30] (* _Harvey P. Dale_, Nov 10 2013 *)

%t a[ n_] := 2^(n + 2) - (2 + Mod[n + 1, 2]) 2^Quotient[n + 1, 2]; (* _Michael Somos_, Jun 24 2018 *)

%o (PARI) {a(n) = 2^(n+2) - (2 + (n+1)%2) * 2^((n+1)\2)}; /* _Michael Somos_, Jun 24 2018 */

%Y Cf. A027383, A052955.

%K nonn,easy

%O 0,2

%A _Mitch Harris_

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Last modified May 23 20:23 EDT 2019. Contains 323528 sequences. (Running on oeis4.)