

A332057


Partial sums (and absolute value of first differences) of A332056: if odd (resp. even) add (resp. subtract) the partial sum to get the next term.


3



1, 3, 2, 3, 7, 4, 5, 11, 6, 7, 15, 8, 9, 19, 10, 11, 23, 12, 13, 27, 14, 15, 31, 16, 17, 35, 18, 19, 39, 20, 21, 43, 22, 23, 47, 24, 25, 51, 26, 27, 55, 28, 29, 59, 30, 31, 63, 32, 33, 67, 34, 35, 71, 36, 37, 75, 38, 39, 79, 40
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OFFSET

1,2


COMMENTS

The terms show a 3quasiperiodic pattern (2m1, 4m1, 2m), m = 1, 2, 3, ...
Or: group positive integers by pairs, then insert the sum of the pair between the two terms.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..19683
Eric Angelini, Re: Add or subtract my cumulative sum of terms, SeqFan list, Feb 24 2020.
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1).


FORMULA

a(3k2) = 2k  1, a(3k1) = 4k  1, a(3k) = 2k, for all k >= 1.
From Colin Barker, Feb 25 2020: (Start)
G.f.: x*(1 + x)*(1 + 2*x + x^3) / ((1  x)^2*(1 + x + x^2)^2).
a(n) = 2*a(n3)  a(n6) for n>6.
(End)


PROG

(PARI) apply( {A332057(n)=n<<max(n%3, 1)\/3}, [1..99])
(PARI) Vec(x*(1 + x)*(1 + 2*x + x^3) / ((1  x)^2*(1 + x + x^2)^2) + O(x^60)) \\ Colin Barker, Feb 26 2020


CROSSREFS

Cf. A332056.
Sequence in context: A007054 A084388 A136389 * A275330 A141863 A071010
Adjacent sequences: A332054 A332055 A332056 * A332058 A332059 A332060


KEYWORD

nonn,easy


AUTHOR

Eric Angelini and M. F. Hasler, Feb 24 2020


STATUS

approved



