A026646 a(n) = Sum_{i=0..n} Sum_{j=0..n} A026637(i,j).

1, 3, 7, 17, 37, 79, 163, 333, 673, 1355, 2719, 5449, 10909, 21831, 43675, 87365, 174745, 349507, 699031, 1398081, 2796181, 5592383, 11184787, 22369597, 44739217, 89478459, 178956943, 357913913, 715827853, 1431655735

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Partial sums of A026644, which are the row sums of A026637. - Paul Barry, Mar 06 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Crossrefs

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

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

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

Programs

Magma

[(2^(n+4) -(6*n+9+(-1)^n))/6: n in [0..40]]; // G. C. Greubel, Jul 01 2024

Mathematica

CoefficientList[Series[(1-x^2+2x^3)/((1-x)(1-2x)(1-x^2)), {x, 0, 29}], x] (* Metin Sariyar, Sep 22 2019 *)
LinearRecurrence[{3,-1,-3,2}, {1,3,7,17}, 41] (* G. C. Greubel, Jul 01 2024 *)

SageMath

[(2^(n+4) - (-1)^n -9 - 6*n)/6 for n in range(41)] # G. C. Greubel, Jul 01 2024

Formula

G.f.: (1 -x^2 +2*x^3)/((1-x)*(1-2*x)*(1-x^2)). - Ralf Stephan, Apr 30 2004

From Paul Barry, Mar 06 2008: (Start)

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

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

a(n+1) = 2*a(n) + A109613(n), a(0)=1. - Paul Curtz, Sep 22 2019