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A217832 Number of sequences of n 2's and 3's with curling number 2 and which have the form XY^2 with Y = 2. 4
0, 1, 1, 2, 4, 8, 16, 32, 63, 126, 252, 502, 1004, 2008, 4012, 8024, 16048, 32089, 64178, 128356, 256696, 513392, 1026784, 2053538, 4107076, 8214152, 16428241, 32856482, 65712964, 131425806, 262851612, 525703224, 1051406197, 2102812394, 4205624788, 8411249081 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Equals A217929 + A217930.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..101

Index entries for sequences related to curling numbers

FORMULA

If n is a multiple of 3 then a(n) = 2a(n-1)-A217929(n/3), otherwise a(n) = 2a(n-1).

Comment from Paul Curtz, Oct 15 2012:

From a(n+3)=1, the terms taken in threes are: 1,2,4, 8,16,32, 63,126,252, ... (*).

a(n+4) - 2*a(n+3) = 0,0,0, 0,0,-1, 0,0,-2, 0,0,-4, 0,0,-7, 0,0,-16, 0,0,-30, 0,0,-63, 0,0,-122,... . See -A217929. This is the formula given above.

2^n - (*) = 0,0,0,0,0,0,1,2,4,10,20,40,84,168,336,679,1358,2716,5448,...

= b(n) with offset 0. Hence a second formula:

b(n+1)-2*b(n)=0,0,0,0,0,1,0,0,2,0,0,4,0,0,7,0,0,16,... . (End)

CROSSREFS

Cf. A217929, A217930, A217931.

Sequence in context: A001592 A194629 A251710 * A251740 A251748 A251762

Adjacent sequences:  A217829 A217830 A217831 * A217833 A217834 A217835

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 15 2012

STATUS

approved

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Last modified November 17 10:07 EST 2018. Contains 317275 sequences. (Running on oeis4.)