A079946 -id:A079946 - cp's OEIS frontend

A091307 a(n)=6*2^n+4 (Bode Number A003461(n+2)) except for a(1)=6.

6, 28, 52, 100, 196, 388, 772, 1540, 3076, 6148, 12292, 24580, 49156, 98308, 196612, 393220, 786436, 1572868, 3145732, 6291460, 12582916, 25165828, 50331652, 100663300, 201326596, 402653188, 805306372, 1610612740, 3221225476, 6442450948, 12884901892

Offset: 1

Alford Arnold, Feb 21 2004

Sequence similar to Bode Numbers relevant to A079946 and numeric partitions.
A053445 describes certain partitions which start triangular arrays of all other numeric partitions; e.g. - 22, 33, 222, 44, 332, 2222, ... A079946 provides the indices for these partitions. (cf. A090324 and A090774).
By expanding the terms of a(n) in a similar manner, the vertex partitions can be readily indexed by noting that the indices increase by eight as follows: 6 28 (one case), 52 60 (two cases), 100 108 116 124 (four cases), 196 204 212 220 228 236 244 252 (eight cases), 388 ...

			a(3) = 52 because we can write 52 = 2*28 - 4.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Except for initial term, same as A003461(n+2). Cf. A053445, A079946, A090774.

CoefficientList[Series[2x (3+5x-10x^2)/((1-x)(1-2x)),{x,0,30}],x] (* or *) LinearRecurrence[{3,-2},{0,6,28,52},40] (* Harvey P. Dale, Sep 01 2021 *)

a(1) = 6, a(2) = 28, a(n) = 2*a(n-1) - 4 for n > 2.

G.f.: 2*x*(3+5*x-10*x^2)/((1-x)*(1-2*x)). - Colin Barker, Mar 12 2012

Edited by M. F. Hasler, Apr 07 2009

A162931 Irregular table which maps each partition of n counted in A162932 to a binary number (converted to decimal).

Original entry on oeis.org

14, 30, 28, 62, 58, 56, 60, 126, 118, 114, 122, 254, 112, 116, 124, 238, 120, 230, 246, 510, 226, 234, 250, 478, 224, 228, 236, 242, 252, 462, 494, 1022

Offset: 6

Alford Arnold, Jul 17 2009

The table encodes each partition of n which satisfies the requirements of A162932 into a binary number with run lengths of 1 determined by the frequency of the parts. As many most-significant-bits are set as determined by the run length of the largest part, each run of 1 is terminated by a 0, and missing parts in the partition are represented by consecutive zeros. Each part in the partition and its frequency pick one member of A079946, and the full binary number is a concatenation of these bits. - R. J. Mathar, Jul 13 2012

			For n=17, the A162932(17)=4 solutions are 2+2+2+2+3+3+3, 2+3+3+3+3+3, 2+3+4+4+4, and 2+5+5+5. These are represented here by
111011110=478 (3 threes give a run length of 3, and four 2's give a run length of 4),
11111010=250 (five 3's give a run length of 5 and one 2 gives a run length of 1),
11101010=234 (three 4's give a run length of 3, one 3 gives a run length of 1 and one 2 gives another run length of 1),
and 11100010=226 (three 5's give a run length of 3, missing 4 and 3 give two run lengths of zero, one 2 give one run length of 1),
then sorted into row 17. - _R. J. Mathar_, Jul 13 2012
A162932 begins 1 0 1 1 1 1 3 1 3 4 4 4 8 6 ... so the table begins
14
.
30
28
62
58
56,60,126
118
114,122,254
112,116,124,238
120,230,246,510
226,234,250,478
224,228,236,242,252,462,494,1022

A162932 (number of entries per row). A079946

cp's OEIS Frontend

A091307 a(n)=6*2^n+4 (Bode Number A003461(n+2)) except for a(1)=6.

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