A137171 - OEIS

%I #9 May 05 2024 17:30:08

%S 0,0,0,1,0,0,1,1,0,1,2,1,1,3,3,1,4,6,4,2,10,10,6,6,20,16,12,16,36,28,

%T 28,36,64,56,64,72,120,120,136,136,240,256,272,256,496,528,528,496,

%U 1024,1056,1024,992,2080,2080,2016,2016,4160,4096,4032,4096,8256,8128,8128

%N Interleaved reading of A000749 and its first to third differences.

%C A000749 is identical to its fourth differences, which implies that the 2nd differences equal the 5th, the 3rd differences the 6th and so on and implies that each of the sequences of these differences obeys the recurrence a(n)=4a(n-1)-6a(n-2)+4a(n-3), n > 3.

%C The table containing A000749 and its first differences (essentially A038505), 2nd differences (A038504) and 3rd differences (A038503) as the 4 rows is

%C O, 0, 0, 1, 4, 10, 20, 36, 64, ...

%C 0, 0, 1, 3, 6, 10, 16, 28, 56, ...

%C 0, 1, 2, 3, 4, 6, 12, 28, 64, ...

%C 1, 1, 1, 1, 2, 6, 16, 36, 72, ...

%C Columns sums are 1, 2, 4, 8, 16, 32 ... = 2^n =A000079. The sequence reads this table column by column.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4).

%t Join[{0, 0, 0, 1},LinearRecurrence[{0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4},{0, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 1},59]] (* _Ray Chandler_, Sep 23 2015 *)

%Y Cf. A137172, A137173.

%K nonn,tabf

%O 0,11

%A _Paul Curtz_, May 11 2008

%E Edited by _R. J. Mathar_, Jun 28 2008