A026646 - OEIS

%I #25 Jul 02 2024 02:45:47

%S 1,3,7,17,37,79,163,333,673,1355,2719,5449,10909,21831,43675,87365,

%T 174745,349507,699031,1398081,2796181,5592383,11184787,22369597,

%U 44739217,89478459,178956943,357913913,715827853,1431655735

%N a(n) = Sum_{i=0..n} Sum_{j=0..n} A026637(i,j).

%C a(n) indexes the corner blocks on the Jacobsthal spiral built from blocks of unit area (using J(1) and J(2) as the sides of the first block). - _Paul Barry_, Mar 06 2008

%C Partial sums of A026644, which are the row sums of A026637. - _Paul Barry_, Mar 06 2008

%H G. C. Greubel, <a href="/A026646/b026646.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).

%F G.f.: (1 -x^2 +2*x^3)/((1-x)*(1-2*x)*(1-x^2)). - _Ralf Stephan_, Apr 30 2004

%F From _Paul Barry_, Mar 06 2008: (Start)

%F a(n) = A001045(n+3) - 2*floor((n+2)/2).

%F a(n) = -n + Sum_{k=0..n} A001045(k+2) = A084639(n+1) - n. (End)

%F a(n+1) = 2*a(n) + A109613(n), a(0)=1. - _Paul Curtz_, Sep 22 2019

%t CoefficientList[Series[(1-x^2+2x^3)/((1-x)(1-2x)(1-x^2)), {x, 0, 29}], x] (* _Metin Sariyar_, Sep 22 2019 *)

%t LinearRecurrence[{3,-1,-3,2}, {1,3,7,17}, 41] (* _G. C. Greubel_, Jul 01 2024 *)

%o (Magma) [(2^(n+4) -(6*n+9+(-1)^n))/6: n in [0..40]]; // _G. C. Greubel_, Jul 01 2024

%o (SageMath) [(2^(n+4) - (-1)^n -9 - 6*n)/6 for n in range(41)] # _G. C. Greubel_, Jul 01 2024

%Y Cf. A000126, A001045, A026637, A026644, A084639, A109613.

%Y Cf. A026637, A026638, A026639, A026640, A026641, A026642, A026643.

%Y Cf. A026644, A026966, A026967, A026968, A026969, A026970.

%K nonn

%O 0,2

%A _Clark Kimberling_