A107663 a(2n) = 2*4^n-1, a(2n+1) = (2^(n+1)+1)^2; interlaces A083420 with A028400.

1, 9, 7, 25, 31, 81, 127, 289, 511, 1089, 2047, 4225, 8191, 16641, 32767, 66049, 131071, 263169, 524287, 1050625, 2097151, 4198401, 8388607, 16785409, 33554431, 67125249, 134217727, 268468225, 536870911, 1073807361, 2147483647

Offset

0,2

Comments

a(2n) = A085903(2n) = A083420(n).

Floretion Algebra Multiplication Program, FAMP Code: 4tesseq[A*B] with A = + .25'i + .25'j + .25'k + .25i' + .25j' + .25k' + .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' + .25'ki' + .25'kj' + .25e and B = + .5'i + .5i' + 'ii' + e [Factor added to formula by Creighton Dement, Dec 11 2009]

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Henry Bottomley, Illustration of initial terms (A028400)

I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.

Index entries for linear recurrences with constant coefficients, signature (1,4,-2,-4).

Formula

G.f.: (-1-8*x+6*x^2+16*x^3) / ((1-2*x)*(x+1)*(2*x^2-1)).

From Colin Barker, May 21 2019: (Start)

a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3) - 4*a(n-4) for n>3.

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

(End)

Prog

(PARI) Vec((1 + 8*x - 6*x^2 - 16*x^3) / ((1 + x)*(1 - 2*x)*(1 - 2*x^2)) + O(x^35)) \\ Colin Barker, May 21 2019

Crossrefs

Cf. A083420, A028400, A062510, A085903.

Sequence in context: A190995 A186830 A124050 * A298780 A231605 A248307

Adjacent sequences: A107660 A107661 A107662 * A107664 A107665 A107666

Keyword

easy,nonn

Author

Creighton Dement, May 19 2005

Status

approved