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A178590 a(2n) = 3*a(n), a(2n+1) = a(n) + a(n+1). 6
1, 3, 4, 9, 7, 12, 13, 27, 16, 21, 19, 36, 25, 39, 40, 81, 43, 48, 37, 63, 40, 57, 55, 108, 61, 75, 64, 117, 79, 120, 121, 243, 124, 129, 91, 144, 85, 111, 100, 189, 103, 120, 97, 171, 112, 165, 163, 324, 169, 183, 136, 225, 139, 192, 181, 351, 196, 237, 199, 360, 241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In groups of 1, 2, 4, 8, ... terms; sums of group terms appears to be A081625: (1, 7, 41, 223,...), for example: 41 = (9 + 7 + 12 + 13).

Equals row 3 in the array shown in A178568, an infinite family of sequences of the form a(2n) = r*a(n), a(2n+1) = a(n) + a(n+1).

Let M = an infinite lower triangular matrix with (1, 3, 1, 0, 0, 0,...) in each column, and with successive columns shifted down twice from the previous column. A178590 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence.

The Stern polynomial B(n,x) evaluated at x=3. See A125184. - T. D. Noe, Feb 28 2011

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8191

FORMULA

a(2n) = 3*a(n), a(2n+1) = a(n) + a(n+1).

a(n) = A090880(A260443(n)). - Antti Karttunen, Jul 29 2015

G.f.: x * Product_{k>=0} (1 + 3*x^(2^k) + x^(2^(k+1))). - Ilya Gutkovskiy, Jul 07 2019

EXAMPLE

In groups of 2^n terms (n=0,1,2,...):

1;

3, 4;

9, 7, 12, 13;

27, 16, 21, 19, 36, 25, 39, 40;

...

a(6) = 12 = 3*a(3) = 3*4

a(7) = 13 = a(3) + a(4) = 4 + 9

MATHEMATICA

a[0] = a[1] = 1; a[n_] := a[n] = If[ OddQ@n, a[(n - 1)/2] + a[(n + 1)/2], 3*a[n/2]]; Array[a, 61] (* Robert G. Wilson v, Jun 11 2010 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A178590 n) (cond ((<= n 1) n) ((even? n) (* 3 (A178590 (/ n 2)))) (else (+ (A178590 (/ (- n 1) 2)) (A178590 (/ (+ n 1) 2))))))

;; Antti Karttunen, Jul 29 2015

CROSSREFS

Row 3 of A178568.

Cf. A081625, A090880, A260443.

Sequence in context: A167531 A062319 A285265 * A022463 A239384 A242219

Adjacent sequences:  A178587 A178588 A178589 * A178591 A178592 A178593

KEYWORD

nonn,look

AUTHOR

Gary W. Adamson, May 29 2010

EXTENSIONS

a(19) onwards from Robert G. Wilson v, Jun 11 2010

STATUS

approved

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Last modified October 17 04:09 EDT 2019. Contains 328106 sequences. (Running on oeis4.)