A164095 - OEIS

A164095

a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

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OFFSET

1,1

COMMENTS

Interleaving of A020714 and A007283 without initial term 3.

Partial sums are in A164096.

Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is A164110.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Jeffrey Shallit, The speed of convergence in greedy Galois games, arXiv:2605.00194 [cs.FL], 2026. See p. 2.

Index entries for linear recurrences with constant coefficients, signature (0,2).

FORMULA

a(n) = A070876(n)/3.

a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(5+6*x)/(1-2*x^2).

MATHEMATICA

LinearRecurrence[{0, 2}, {5, 6}, 50] (* Harvey P. Dale, Aug 15 2020 *)

(* Alternative: *)

With[{nn=20}, Riffle[NestList[ 2#&, 5, nn], NestList[2#&, 6, nn]]] (* Harvey P. Dale, Aug 15 2020 *)