A136383
Sequence A136382 shown in octal base.
Original entry on oeis.org
6, 50, 5660, 57266500, 5745056664272600, 57725105055132666451322727325000, 5774565132122505051225325134566664426132512553272725535132426000, 57772261341352513254262525526505050275531226553251312456427326666445105642653132512245531220572727245225254562513252136134550000
Offset: 1
A036284
Periodic vertical binary vectors of Fibonacci numbers.
Original entry on oeis.org
6, 24, 1440, 5728448, 92568198012160, 26494530374406845814111659520, 2095920895719545919920115988669687683503034097906010941440, 13128614603426246034591796912897206548807135027496968025827278400248602613784037111736380004928525614173642247188480
Offset: 0
When Fibonacci numbers are written in binary (see A004685), under each other as:
0000000 (0)
0000001 (1)
0000001 (1)
0000010 (2)
0000011 (3)
0000101 (5)
0001000 (8)
0001101 (13)
0010101 (21)
0100010 (34)
0110111 (55)
1011001 (89)
it can be seen that the bits in the n-th column from right repeat after a period of A007283(n): 3, 6, 12, 24, ... (See also A001175). This sequence is formed from those bits: 011, reversed is 110, is binary for 6, thus a(0) = 6. 000110, reversed is 11000, is binary for 24, thus a(1) = 24, 000001011010, reversed is 10110100000, is binary for 1440, thus a(2) = 1440.
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A036284:=proc(n) option remember; local a, b, c, i, j, k, l, s, x, y, z; if (0 = n) then (6) else a := 0; b := 0; s := 0; x := 0; y := 0; k := 3*(2^(n-1)); l := 3*(2^n); j := 0; for i from 0 to l do z := bit_i(A036284(n-1),(j)); c := (a + b + (`if`((x = y),x,(z+1))) mod 2); if(c <> 0) then s := s + (2^i); fi; a := b; b := c; x := y; y := z; j := j + 1; if(j = k) then j := 0; fi; od; RETURN(s); fi; end:
bit_i := (x,i) -> `mod`(floor(x/(2^i)),2);
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a[n_] := Sum[Mod[Fibonacci[k]/2^n // Floor, 2]* 2^k, {k, 0, 3*2^n - 1}]; Table[a[n], {n, 0, 7}] (* Jean-François Alcover, Mar 04 2016 *)
Entry revised Dec 29 2007
A136380
Quotient obtained when A036284(n) is considered as a GF(2)[X]-polynomial and it is divided by (x^3 + 1) ^ A000225(n-1).
Original entry on oeis.org
24, 160, 11968, 49657088, 837028380268032, 237269922100748727235760269312, 18811253173629696438994877569412700111469395859003555753984, 118178826602781220665226658680265194908312590801831513776333330179329649495708436476846379030238467286212637486694400
Offset: 1
A136384
Quotient obtained when A136380(n)/2 is considered as a GF(2)[X]-polynomial and it is divided by (x + 1).
Original entry on oeis.org
4, 48, 3360, 14043520, 233515838757120, 65982595605873500894008888320, 5233741023536997251047595348728205456443682897303843358720, 32837130684987081672210288030183520098814938795984162933658101468543499651419210151303128996446334767341864627691520
Offset: 1
A136386
Quotient obtained when A037097(n) is considered as a GF(2)[X]-polynomial and it is divided by (x + 1) ^ A000225(n-1) (= A051179(n-2)).
Original entry on oeis.org
4, 8, 352, 3728, 7269662752, 761166466256046848, 390022035611646394530728097023856870592, 91600670557117582933643002658167825054614175029432880501373395030525438396928, 13417853484388319477475698658536993288839029124735549539652836318808118017743106800015257954250357092148394821846783842030516713870361254572407216621548672
Offset: 3
Showing 1-5 of 5 results.
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