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

Author

Creighton Dement, May 19 2005

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A083420, A028400, A062510, A085903.

Programs

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

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)