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A115362 Row sums of ((1,x) + (x,x^2))^(-1)*((1,x)-(x,x^2))^(-1) (using Riordan array notation). 3
1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row sums of the matrix product A115358*A115361.

Generalized Ruler Function for k=4. - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)

a(n) is 1 + the 4-adic valuation of n+1. - Joerg Arndt, Oct 07 2015

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16384

FORMULA

G.f.: A(x) = Sum_k>=0} x^(4^k)/(1-x^(4^k)). - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)

Dirichlet g.f. (conjectured): zeta(s)/(1-2^(-2s)). - Ralf Stephan, Mar 27 2015

a(n) = (1/3)*(4 + A053737(n) - A053737(n+1)). - Tom Edgar, Oct 06 2015

a(4*n) = a(4*n+1) = a(4*n+2) = 1, a(4*n+3) = 1+a(n), if n >= 0. - Michael Somos, Jul 13 2017

a(n) = 1 + A235127(1+n). - Antti Karttunen, Nov 18 2017, after Joerg Arndt's Oct 07 2015 comment.

MATHEMATICA

a[ n_] := If[ n < 0, 0, 1 + IntegerExponent[n + 1, 4]]; (* Michael Somos, Jul 19 2017 *)

PROG

(Sage) [(1/3)*(4-sum(n.digits(4))+sum((n-1).digits(4))) for n in [1..96]] # Tom Edgar, Oct 06 2015

(PARI) a(n) = 1 + valuation(n+1, 4); \\ Joerg Arndt, Oct 07 2015

(PARI) {a(n) = if( n<0, 0, n%4==3, 1 + a((n - 3) / 4), 1)}; /* Michael Somos, Jul 13 2017 */

CROSSREFS

Cf. A053737, A115358, A115361, A235127.

Sequence in context: A161102 A276329 A161101 * A277872 A161100 A053543

Adjacent sequences:  A115359 A115360 A115361 * A115363 A115364 A115365

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jan 21 2006

STATUS

approved

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)