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A107663 a(2n) = 2*4^n-1, a(2n+1) = (2^(n+1)+1)^2; interlaces A083420 with A028400. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

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

H. 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

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]

(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

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Last modified June 25 03:58 EDT 2019. Contains 324338 sequences. (Running on oeis4.)